library(igraph)
library(knitr)
library(corrplot)
library(tidyverse)
library(geojsonio)
library(stplanr)
library(leaflet)
library(rprojroot)
library(kableExtra)
library(sf)
::opts_chunk$set(echo = TRUE)
knitr
# This is the project path
<- find_rstudio_root_file() path
Network analysis practical: networks of cities
Resources
Some of the materials for this tutorial have been adapted from:
Philosophy of this RMarkdown
document
As you can see this is a long .Rmd
document, which has a dual objective. On one hand, it will help you achieve the unit learning outcomes as it provides an implementation of most of the concepts and ideas we discuss for this unit. On the other hand this is almost a representation of a ‘real world’ workflow. Instead of breaking the code in shorter and maybe more digestible .Rmd
documents I decided to provide you with a working sequence of all actions I would have taken in order to analyse a network with spatial dimensions such as the network of commuting flows in \(2011\). You can use this workflow as the basis for building your own approach and, consequently, code in order to complete this session’s project. We will spend at least \(2\) sessions to go through this code.
To begin with, create a new RStudio Project
as a new directory (File > New Project…) and within it create a source
and data
directory to store the code and the data accordingly. Instructions on how to create such a project, can be found here. Then, create a new RMarkdown
document to implement all the below.
Install and load packages
We will use quite a few packages for this tutorial. Most of the code is based on the tidyverse
logic – see here for more info. But the main package we will use for network data wrangling and analysis is igraph
– more info here.
Important
The below code snippet assumes that all the packages are installed. If you are using a university PC they are probably not. If they are not installed, you need to do so by using install.packages("package.name")
.
Commuting data and networks
For this tutorial we will use travel to work data from the 2011 UK Census. The data is available online, but it requires an academic login. After you log in, download the WU03UK element, save the .csv on your working directory under a /data
directory and unzip it. We will use the:
Location of usual residence and place of work by method of travel to work
for
Census Merged local authority districts in England and Wales, Council areas in Scotland, Local government districts in Northern Ireland.
The below code loads the data.
<- paste0(path, "/data/wu03uk_v3/wu03uk_v3.csv")
path.data <- read_csv(path.data)
commuting glimpse(commuting)
As you may have noticed, the commuting
object includes only the codes for the local authorities. Let’s try to see these codes.
First for the origins.
%>% distinct(`Area of usual residence`) commuting
# A tibble: 404 × 1
`Area of usual residence`
<chr>
1 95AA
2 95BB
3 95CC
4 95DD
5 95EE
6 95FF
7 95GG
8 95HH
9 95II
10 95JJ
# ℹ 394 more rows
And the same for the destinations (results omitted).
%>% distinct(`Area of workplace`) commuting
Question: Can you guess the countries these codes refer to?
You might have observe some weird codes (OD0000001, OD0000002, OD0000003 and OD0000004). With some simple Google searching we can find the 2011 Census Origin-Destination Data User Guide, which indicates that these codes do not refer to local authorities:
OD0000001 = Mainly work at or from home
OD0000002 = Offshore installation
OD0000003 = No fixed place
OD0000004 = Outside UK
For the sake of simplicity we will remove these non-geographical nodes.
<- c("OD0000001", "OD0000002", "OD0000003", "OD0000004")
non.la <- commuting %>%
commuting filter(!`Area of workplace` %in% non.la)
Check the %in%
operator. Also !
represents negation.
Now let’s do some clean-up of the commuting
data frame. Let’s remind ourselves how the data look like.
glimpse(commuting)
Rows: 108,546
Columns: 14
$ `Area of usual residence` <chr> "95AA", "95AA", "95AA", "95…
$ `Area of workplace` <chr> "95AA", "95BB", "95CC", "95…
$ `All categories: Method of travel to work` <dbl> 9465, 107, 42, 1485, 35, 18…
$ `Work mainly at or from home` <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ `Underground, metro, light rail, tram` <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ Train <dbl> 12, 0, 0, 11, 0, 0, 165, 1,…
$ `Bus, minibus or coach` <dbl> 243, 1, 1, 84, 1, 0, 434, 1…
$ Taxi <dbl> 421, 2, 0, 13, 0, 0, 14, 0,…
$ `Motorcycle, scooter or moped` <dbl> 58, 0, 0, 8, 0, 0, 23, 0, 0…
$ `Driving a car or van` <dbl> 5376, 68, 29, 1111, 25, 12,…
$ `Passenger in a car or van` <dbl> 1721, 20, 9, 241, 9, 4, 830…
$ Bicycle <dbl> 196, 5, 0, 2, 0, 0, 11, 0, …
$ `On foot` <dbl> 1403, 9, 3, 13, 0, 2, 46, 1…
$ `Other method of travel to work` <dbl> 35, 2, 0, 2, 0, 0, 6, 0, 1,…
We are only keeping the English and Wales local authorities by keeping the observations with a local authority code starting from E (for England) and W (for Wales).
<- commuting %>% filter(startsWith(`Area of usual residence`, "E") |
commuting startsWith(`Area of usual residence`, "W")) %>%
filter(startsWith(`Area of workplace`, "E") |
startsWith(`Area of workplace`, "W")) %>%
glimpse()
Rows: 93,034
Columns: 14
$ `Area of usual residence` <chr> "E41000001", "E41000001", "…
$ `Area of workplace` <chr> "E41000001", "E41000002", "…
$ `All categories: Method of travel to work` <dbl> 20777, 1591, 534, 3865, 433…
$ `Work mainly at or from home` <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ `Underground, metro, light rail, tram` <dbl> 6, 1, 0, 1, 0, 0, 0, 0, 0, …
$ Train <dbl> 26, 32, 0, 49, 11, 0, 0, 0,…
$ `Bus, minibus or coach` <dbl> 1922, 140, 21, 167, 7, 0, 0…
$ Taxi <dbl> 527, 11, 4, 20, 1, 0, 0, 0,…
$ `Motorcycle, scooter or moped` <dbl> 107, 6, 6, 23, 4, 0, 0, 0, …
$ `Driving a car or van` <dbl> 11788, 1225, 448, 3144, 360…
$ `Passenger in a car or van` <dbl> 1965, 99, 36, 365, 33, 0, 0…
$ Bicycle <dbl> 593, 13, 1, 29, 2, 0, 0, 0,…
$ `On foot` <dbl> 3789, 60, 16, 60, 15, 0, 0,…
$ `Other method of travel to work` <dbl> 54, 4, 2, 7, 0, 0, 0, 0, 0,…
We can also see we many rows we dropped with glimpse()
.
It is very important to distinguish between intra- and inter-local authority flows. In network analysis terms, these are the values we find on the diagonal of an adjacency matrix and refer to the commuting flows within a specific local authority or between different ones. For this exercise we are dropping the intra-local authority flows. Although not used here, we also create a new object with the intra-local authority flows.
<- commuting %>%
commuting.intra filter(`Area of usual residence` == `Area of workplace`)
<- commuting %>%
commuting filter(`Area of usual residence` != `Area of workplace`) %>%
glimpse()
Rows: 92,688
Columns: 14
$ `Area of usual residence` <chr> "E41000001", "E41000001", "…
$ `Area of workplace` <chr> "E41000002", "E41000003", "…
$ `All categories: Method of travel to work` <dbl> 1591, 534, 3865, 433, 5, 2,…
$ `Work mainly at or from home` <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ `Underground, metro, light rail, tram` <dbl> 1, 0, 1, 0, 0, 0, 0, 0, 0, …
$ Train <dbl> 32, 0, 49, 11, 0, 0, 0, 0, …
$ `Bus, minibus or coach` <dbl> 140, 21, 167, 7, 0, 0, 0, 1…
$ Taxi <dbl> 11, 4, 20, 1, 0, 0, 0, 0, 0…
$ `Motorcycle, scooter or moped` <dbl> 6, 6, 23, 4, 0, 0, 0, 0, 0,…
$ `Driving a car or van` <dbl> 1225, 448, 3144, 360, 5, 2,…
$ `Passenger in a car or van` <dbl> 99, 36, 365, 33, 0, 0, 0, 0…
$ Bicycle <dbl> 13, 1, 29, 2, 0, 0, 0, 0, 0…
$ `On foot` <dbl> 60, 16, 60, 15, 0, 0, 0, 0,…
$ `Other method of travel to work` <dbl> 4, 2, 7, 0, 0, 0, 0, 0, 0, …
Please note the constant use of glimpse()
to keep control of how many observations we have and check if we missed anything.
Also, take a note of the commuting
object, which includes multiple types of commuting flows. Therefore, we will build \(3\) different networks:
one for all the commuting flows
one only for train flows
one only for bicycle flows.
<- commuting %>%
commuting.all select(`Area of usual residence`,
`Area of workplace`,
`All categories: Method of travel to work`) %>%
rename(o = `Area of usual residence`, # Area of usual residence is annoyingly
d = `Area of workplace`, # long, so I am renaiming theses columns.
weight = `All categories: Method of travel to work`)
# just FYI this is how you could have achieved the same output using base R
# instead of dplyr of the tidyverse ecosystem
# commuting.all <- commuting[,1:3]
# names(commuting.all)[1] <- "o"
# names(commuting.all)[2] <- "d"
# names(commuting.all)[3] <- "weight"
<- commuting %>%
commuting.train select(`Area of usual residence`,
`Area of workplace`,
`All categories: Method of travel to work`,
`Train`) %>%
rename(o = `Area of usual residence`,
d = `Area of workplace`,
weight = `All categories: Method of travel to work`) %>%
# The below code drops all the lines with 0 train flows in order to exclude
# these edges from the network.
filter(Train!=0)
<- commuting %>%
commuting.bicycle select(`Area of usual residence`,
`Area of workplace`,
`All categories: Method of travel to work`,
`Bicycle`) %>%
rename(o = `Area of usual residence`,
d = `Area of workplace`,
weight = `All categories: Method of travel to work`) %>%
# The below code drops all the lines with 0 bicycle flows in order to exclude
# these edges from the network.
filter(Bicycle!=0)
Unless you know the local authority codes by hard, it might be useful to also add the corresponding local authority names. These can be easily obtained from the ONS’s Open Geography portal. The below code directly downloads a GeoJSON
file with the local authorities in England and Wales. If you don’t know what a GeoJSON
file is, have a look here. Boundary data can also be obtained by UK Data Service.
For the time being we are only interested in the local authority names and codes. We will use the spatial object later.
Tip: the below code downloads the GeoJSON
file over the web. If you want to run the code multiple times, it might be faster to download the file ones, save it on your hard drive and the point this location to st_read()
.
<-st_read("https://services1.arcgis.com/ESMARspQHYMw9BZ9/arcgis/rest/services/CMLAD_Dec_2011_SGCB_GB_2022/FeatureServer/0/query?outFields=*&where=1%3D1&f=geojson")
la glimpse(la)
<- as.data.frame(la) %>%
la.names select(cmlad11cd, cmlad11nm) # all we need is the LA names and codes
The next step is to actually create the network objects. The below code creates the igraph
network objects using the graph_from_data_frame()
function as we already have all the necessary data in data frames (commuting.all
, commuting.train
and commuting.bicycle
). We then attach the local authority names as an attribute to these networks.
<-graph_from_data_frame(commuting.all, directed = TRUE, vertices = la.names)
net.all
<-graph_from_data_frame(commuting.train, directed = TRUE, vertices = la.names)
net.train
<-graph_from_data_frame(commuting.bicycle, directed = TRUE, vertices = la.names) net.bicycle
Network attributes
The below igraph
functions illustrate some attributes of the network with all the flows.
# It provides information about the type of the net.all object. Not surprisingly,
# it is an igraph network.
class(net.all)
[1] "igraph"
# It displays the network file, the number of nodes and edges (345 and 92,688
# in this case).
net.all
IGRAPH 73bdbf9 DNW- 346 92688 --
+ attr: name (v/c), cmlad11nm (v/c), weight (e/n)
+ edges from 73bdbf9 (vertex names):
[1] E41000001->E41000002 E41000001->E41000003 E41000001->E41000004
[4] E41000001->E41000005 E41000001->E41000006 E41000001->E41000007
[7] E41000001->E41000009 E41000001->E41000010 E41000001->E41000011
[10] E41000001->E41000012 E41000001->E41000013 E41000001->E41000014
[13] E41000001->E41000015 E41000001->E41000016 E41000001->E41000017
[16] E41000001->E41000018 E41000001->E41000019 E41000001->E41000020
[19] E41000001->E41000021 E41000001->E41000022 E41000001->E41000023
[22] E41000001->E41000025 E41000001->E41000026 E41000001->E41000029
+ ... omitted several edges
# It displays the vertices (aka nodes)
V(net.all)
+ 346/346 vertices, named, from 73bdbf9:
[1] E41000001 E41000002 E41000003 E41000004 E41000005 E41000006 E41000007
[8] E41000008 E41000009 E41000010 E41000011 E41000012 E41000013 E41000014
[15] E41000015 E41000016 E41000017 E41000018 E41000019 E41000020 E41000021
[22] E41000022 E41000023 E41000024 E41000025 E41000026 E41000027 E41000028
[29] E41000029 E41000030 E41000031 E41000032 E41000033 E41000034 E41000035
[36] E41000036 E41000037 E41000038 E41000039 E41000040 E41000041 E41000042
[43] E41000043 E41000044 E41000045 E41000046 E41000047 E41000048 E41000049
[50] E41000050 E41000051 E41000052 E41000053 E41000054 E41000055 E41000056
[57] E41000057 E41000058 E41000059 E41000060 E41000061 E41000062 E41000063
[64] E41000064 E41000065 E41000066 E41000067 E41000068 E41000069 E41000070
+ ... omitted several vertices
# It displays the vertex attributes. In this case the local authority codes.
vertex_attr(net.all) %>% glimpse()
List of 2
$ name : chr [1:346] "E41000001" "E41000002" "E41000003" "E41000004" ...
$ cmlad11nm: chr [1:346] "Hartlepool" "Middlesbrough" "Redcar and Cleveland" "Stockton-on-Tees" ...
# the output of vertex_attr() is quite long, this is why I chained it with glimpse()
# It displays the edges.
E(net.all) %>% glimpse()
'igraph.es' int [1:92688] 1 2 3 4 5 6 7 8 9 10 ...
- attr(*, "is_all")= logi TRUE
- attr(*, "vnames")= chr [1:92688] "E41000001|E41000002" "E41000001|E41000003" "E41000001|E41000004" "E41000001|E41000005" ...
- attr(*, "env")=<weakref>
- attr(*, "graph")= chr "73bdbf94-587f-422d-9ba1-1eb7fe4b7683"
# the output of E() is quite long, this is why I chained it with glimpse()
# It displays the weights for each edge. In our case the weights represent commuters.
edge.attributes(net.all)$weight %>% glimpse()
num [1:92688] 1591 534 3865 433 5 ...
# as above re: glimpse()
# Asks whether the network is weighted or not
is.weighted(net.all)
Warning: `is.weighted()` was deprecated in igraph 2.0.0.
ℹ Please use `is_weighted()` instead.
[1] TRUE
Question: How many nodes and edges are there for the other types of networks? What do these differences mean?
Network measures
The below igraph
functions calculate some simple network measures. Have a look at the lecture slides and the reference list to remind yourselves.
# Network diameter. We do not consider the weights because it affects the measurement.
<- diameter(net.all, directed = TRUE, weights = NA)
d.all d.all
[1] 2
# Average path length
<- mean_distance(net.all)
mean_ditst.all mean_ditst.all
[1] 1.895552
# Network density
<- edge_density(net.all)
dens.all dens.all
[1] 0.7764765
# Clustering Coefficient or Transitivity
<- transitivity(net.all)
trans.all trans.all
[1] 0.9221811
# Reciprocity
<- reciprocity(net.all)
rec.all rec.all
[1] 0.8297298
# Assortativity
<- assortativity_degree(net.all, directed = T)
ass.all ass.all
[1] -0.08068428
Question: Do the same for the other types of commuting networks and compare the different measures. Why do we observe these differences?
Centralities
Now we are moving from network-level measures to some node-level ones. Specifically, we will calculate different centrality measures.
# Binary in-degree centrality.
<- degree(net.all, mode = "in")
in.degree head(in.degree)
E41000001 E41000002 E41000003 E41000004 E41000005 E41000006
111 214 118 216 237 275
# Binary out-degree centrality.
<- degree(net.all, mode = "out")
out.degree head(out.degree)
E41000001 E41000002 E41000003 E41000004 E41000005 E41000006
231 250 242 292 258 274
# Binary degree centrality.
<- degree(net.all, mode = "all")
degree head(degree)
E41000001 E41000002 E41000003 E41000004 E41000005 E41000006
342 464 360 508 495 549
# The function graph.strength() calculates the weighted degree centrality.
# Weighed in-degree centrality.
<- graph.strength(net.all, mode = "in") w.in.degree
Warning: `graph.strength()` was deprecated in igraph 2.0.0.
ℹ Please use `strength()` instead.
head(w.in.degree)
E41000001 E41000002 E41000003 E41000004 E41000005 E41000006
8360 30038 12786 29986 18445 23080
# Weighed out-degree centrality.
<- graph.strength(net.all, mode = "out")
w.out.degree head(w.out.degree)
E41000001 E41000002 E41000003 E41000004 E41000005 E41000006
11261 20664 21904 29329 15036 22981
# Weighed degree centrality.
<- graph.strength(net.all, mode = "all")
w.degree head(w.degree)
E41000001 E41000002 E41000003 E41000004 E41000005 E41000006
19621 50702 34690 59315 33481 46061
# The function betweenness() calculates betweenness centrality. As before.
<- betweenness(net.all, weights = NA)
btwnss head(btwnss)
E41000001 E41000002 E41000003 E41000004 E41000005 E41000006
21.38152 53.13953 23.46728 65.89576 63.64096 82.81950
# Eigenvector centrality.
<- eigen_centrality(net.all)
eigen
# Be careful, eigen has a more complicated structure. Use ?eigen_central to read more.
# Before goin. forward, let's see the structure of eigen.
str(eigen)
List of 3
$ vector : Named num [1:346] 0.00039 0.000679 0.000459 0.0011 0.000703 ...
..- attr(*, "names")= chr [1:346] "E41000001" "E41000002" "E41000003" "E41000004" ...
$ value : num 2e+05
$ options:List of 20
..$ bmat : chr "I"
..$ n : int 346
..$ which : chr "LA"
..$ nev : int 1
..$ tol : num 0
..$ ncv : int 0
..$ ldv : int 0
..$ ishift : int 1
..$ maxiter: int 3000
..$ nb : int 1
..$ mode : int 1
..$ start : int 1
..$ sigma : num 0
..$ sigmai : num 0
..$ info : int 0
..$ iter : int 2
..$ nconv : int 1
..$ numop : int 30
..$ numopb : int 0
..$ numreo : int 21
# We are interested in eigen$vector.
head(eigen$vector)
E41000001 E41000002 E41000003 E41000004 E41000005 E41000006
0.0003901039 0.0006790253 0.0004593193 0.0010995296 0.0007032769 0.0012432240
# page rank centrality.
<- page_rank(net.all, directed = T)
prank str(prank) # as before
List of 3
$ vector : Named num [1:346] 0.00109 0.00296 0.00178 0.00318 0.00181 ...
..- attr(*, "names")= chr [1:346] "E41000001" "E41000002" "E41000003" "E41000004" ...
$ value : num 1
$ options: NULL
head(prank$vector)
E41000001 E41000002 E41000003 E41000004 E41000005 E41000006
0.001088677 0.002963743 0.001784703 0.003183087 0.001807346 0.002157680
Now that we understood how the above works, let’s chain them together to create a centralities
tibble.
<- tibble(
centralities names = vertex_attr(net.all)[[2]],
# The above creates a vector with the nodes names (i.e. the local authority names).
# We are interested in the second elements of the vertex_attr() as the first one
# includes the local authority codes. Try str(vertex_attr(net.all)) to see why.
# the double squared brackets [[]] brings the vertex, while the single one []
# would have brought a list.
in.degree = degree(net.all, mode = "in"),
out.degree = degree(net.all, mode = "out"),
degree = degree(net.all, mode = "in"),
w.in.degree = graph.strength(net.all, mode = "in"),
w.out.degree = graph.strength(net.all, mode = "out"),
w.degree = graph.strength(net.all, mode = "all"),
btwnss = betweenness(net.all, weights = NA),
eigen = eigen_centrality(net.all)$vector, # note the $vector
prank = page_rank(net.all, directed = T)$vector) %>%
glimpse()
Rows: 346
Columns: 10
$ names <chr> "Hartlepool", "Middlesbrough", "Redcar and Cleveland", "S…
$ in.degree <dbl> 111, 214, 118, 216, 237, 275, 326, 204, 178, 292, 292, 21…
$ out.degree <dbl> 231, 250, 242, 292, 258, 274, 302, 245, 246, 298, 326, 28…
$ degree <dbl> 111, 214, 118, 216, 237, 275, 326, 204, 178, 292, 292, 21…
$ w.in.degree <dbl> 8360, 30038, 12786, 29986, 18445, 23080, 49172, 23988, 19…
$ w.out.degree <dbl> 11261, 20664, 21904, 29329, 15036, 22981, 34607, 19666, 1…
$ w.degree <dbl> 19621, 50702, 34690, 59315, 33481, 46061, 83779, 43654, 3…
$ btwnss <dbl> 21.38152, 53.13953, 23.46728, 65.89576, 63.64096, 82.8195…
$ eigen <dbl> 0.0003901039, 0.0006790253, 0.0004593193, 0.0010995296, 0…
$ prank <dbl> 0.001088677, 0.002963743, 0.001784703, 0.003183087, 0.001…
Or, if you want a nicer table, you can use kable()
. Tip check out the kableExtra
package for more options
%>% kable(caption = "Centralities") %>%
centralities # The following `kableExtra` function introduces a scroll box
scroll_box(width = "100%", height = "300px")
names | in.degree | out.degree | degree | w.in.degree | w.out.degree | w.degree | btwnss | eigen | prank |
---|---|---|---|---|---|---|---|---|---|
Hartlepool | 111 | 231 | 111 | 8360 | 11261 | 19621 | 21.38152 | 0.0003901 | 0.0010887 |
Middlesbrough | 214 | 250 | 214 | 30038 | 20664 | 50702 | 53.13953 | 0.0006790 | 0.0029637 |
Redcar and Cleveland | 118 | 242 | 118 | 12786 | 21904 | 34690 | 23.46728 | 0.0004593 | 0.0017847 |
Stockton-on-Tees | 216 | 292 | 216 | 29986 | 29329 | 59315 | 65.89576 | 0.0010995 | 0.0031831 |
Darlington | 237 | 258 | 237 | 18445 | 15036 | 33481 | 63.64096 | 0.0007033 | 0.0018073 |
Halton | 275 | 274 | 275 | 23080 | 22981 | 46061 | 82.81950 | 0.0012432 | 0.0021577 |
Warrington | 326 | 302 | 326 | 49172 | 34607 | 83779 | 124.18728 | 0.0028033 | 0.0038653 |
Blackburn with Darwen | 204 | 245 | 204 | 23988 | 19666 | 43654 | 46.17387 | 0.0006750 | 0.0024693 |
Blackpool | 178 | 246 | 178 | 19835 | 17775 | 37610 | 43.94347 | 0.0005901 | 0.0025846 |
Kingston upon Hull, City of | 292 | 298 | 292 | 38602 | 24199 | 62801 | 102.14345 | 0.0012955 | 0.0025353 |
East Riding of Yorkshire | 292 | 326 | 292 | 30194 | 54386 | 84580 | 120.56251 | 0.0020021 | 0.0031038 |
North East Lincolnshire | 219 | 286 | 219 | 11562 | 10600 | 22162 | 65.06108 | 0.0007256 | 0.0013687 |
North Lincolnshire | 249 | 297 | 249 | 14755 | 15493 | 30248 | 83.06742 | 0.0007716 | 0.0016239 |
York | 304 | 310 | 304 | 25651 | 21058 | 46709 | 117.86975 | 0.0023097 | 0.0026595 |
Derby | 316 | 308 | 316 | 41670 | 29802 | 71472 | 113.83201 | 0.0029402 | 0.0032790 |
Leicester | 328 | 311 | 328 | 67191 | 41007 | 108198 | 121.94219 | 0.0045364 | 0.0060454 |
Rutland | 223 | 225 | 223 | 6776 | 6446 | 13222 | 40.36699 | 0.0012338 | 0.0010011 |
Nottingham | 336 | 315 | 336 | 89650 | 38180 | 127830 | 134.64542 | 0.0039334 | 0.0059435 |
Herefordshire, County of | 306 | 292 | 306 | 10786 | 13434 | 24220 | 103.12522 | 0.0019351 | 0.0013338 |
Telford and Wrekin | 324 | 296 | 324 | 23376 | 18322 | 41698 | 109.90081 | 0.0018745 | 0.0020630 |
Stoke-on-Trent | 313 | 309 | 313 | 40031 | 33667 | 73698 | 114.84293 | 0.0015778 | 0.0029178 |
Bath and North East Somerset | 318 | 289 | 318 | 29241 | 23945 | 53186 | 106.11349 | 0.0063148 | 0.0031748 |
Bristol, City of | 338 | 324 | 338 | 80907 | 54120 | 135027 | 146.21380 | 0.0085801 | 0.0081482 |
North Somerset | 288 | 309 | 288 | 18813 | 32553 | 51366 | 106.51079 | 0.0033370 | 0.0024983 |
South Gloucestershire | 342 | 315 | 342 | 59359 | 53569 | 112928 | 143.90381 | 0.0071708 | 0.0067618 |
Plymouth | 332 | 300 | 332 | 25793 | 20138 | 45931 | 124.45365 | 0.0015797 | 0.0032944 |
Torbay | 191 | 252 | 191 | 8569 | 12764 | 21333 | 46.76698 | 0.0007531 | 0.0015136 |
Bournemouth | 248 | 283 | 248 | 25210 | 32998 | 58208 | 72.37210 | 0.0044016 | 0.0028426 |
Poole | 314 | 276 | 314 | 32048 | 24563 | 56611 | 87.92048 | 0.0045316 | 0.0030996 |
Swindon | 334 | 293 | 334 | 23868 | 24439 | 48307 | 112.57493 | 0.0066072 | 0.0024599 |
Peterborough | 337 | 294 | 337 | 32552 | 19136 | 51688 | 111.41706 | 0.0080528 | 0.0029620 |
Luton | 341 | 293 | 341 | 34348 | 33348 | 67696 | 117.08185 | 0.0292726 | 0.0026121 |
Southend-on-Sea | 247 | 260 | 247 | 20661 | 29749 | 50410 | 57.62656 | 0.0460325 | 0.0012049 |
Thurrock | 281 | 268 | 281 | 21804 | 34873 | 56677 | 75.03469 | 0.0589668 | 0.0013440 |
Medway | 308 | 312 | 308 | 22710 | 50453 | 73163 | 109.01019 | 0.0533814 | 0.0015706 |
Bracknell Forest | 336 | 263 | 336 | 28503 | 31002 | 59505 | 84.64837 | 0.0181350 | 0.0026867 |
West Berkshire | 340 | 277 | 340 | 33558 | 28003 | 61561 | 103.72536 | 0.0157734 | 0.0033439 |
Reading | 332 | 289 | 332 | 42267 | 32715 | 74982 | 112.58266 | 0.0227425 | 0.0040357 |
Slough | 335 | 271 | 335 | 39282 | 31753 | 71035 | 94.80244 | 0.0380361 | 0.0041691 |
Windsor and Maidenhead | 341 | 273 | 341 | 36971 | 34482 | 71453 | 99.72553 | 0.0372343 | 0.0038264 |
Wokingham | 340 | 269 | 340 | 30764 | 42810 | 73574 | 90.37405 | 0.0237476 | 0.0032668 |
Milton Keynes | 344 | 307 | 344 | 44450 | 27780 | 72230 | 122.22514 | 0.0253813 | 0.0035232 |
Brighton and Hove | 297 | 287 | 297 | 31879 | 36938 | 68817 | 88.44945 | 0.0325543 | 0.0022023 |
Portsmouth | 343 | 288 | 343 | 41272 | 27862 | 69134 | 115.85177 | 0.0059324 | 0.0032274 |
Southampton | 321 | 300 | 321 | 41891 | 41234 | 83125 | 115.21255 | 0.0069496 | 0.0036577 |
Isle of Wight | 219 | 244 | 219 | 2083 | 4544 | 6627 | 44.65755 | 0.0019493 | 0.0006276 |
County Durham | 316 | 328 | 316 | 35081 | 64602 | 99683 | 136.76168 | 0.0025184 | 0.0033631 |
Northumberland | 287 | 310 | 287 | 22254 | 43011 | 65265 | 105.96942 | 0.0024251 | 0.0023084 |
Cheshire East | 331 | 334 | 331 | 53260 | 51773 | 105033 | 153.00249 | 0.0049410 | 0.0044883 |
Cheshire West and Chester | 323 | 324 | 323 | 50910 | 51970 | 102880 | 141.77478 | 0.0034742 | 0.0039760 |
Shropshire | 336 | 330 | 336 | 29111 | 34424 | 63535 | 148.35300 | 0.0036140 | 0.0027990 |
Cornwall,Isles of Scilly | 341 | 330 | 341 | 11163 | 18567 | 29730 | 155.46166 | 0.0032429 | 0.0016854 |
Wiltshire | 345 | 331 | 345 | 39717 | 55625 | 95342 | 160.51941 | 0.0150479 | 0.0040658 |
Bedford | 314 | 297 | 314 | 21392 | 22483 | 43875 | 100.59431 | 0.0154519 | 0.0018139 |
Central Bedfordshire | 343 | 312 | 343 | 32469 | 66131 | 98600 | 129.24999 | 0.0390917 | 0.0028629 |
Aylesbury Vale | 330 | 303 | 330 | 19831 | 34981 | 54812 | 113.28702 | 0.0227757 | 0.0020113 |
Chiltern | 253 | 234 | 253 | 13391 | 22558 | 35949 | 44.70020 | 0.0301093 | 0.0015106 |
South Bucks | 310 | 223 | 310 | 20603 | 20381 | 40984 | 55.75605 | 0.0262182 | 0.0023714 |
Wycombe | 339 | 283 | 339 | 27246 | 32323 | 59569 | 100.06675 | 0.0304376 | 0.0027075 |
Cambridge | 312 | 250 | 312 | 51240 | 16062 | 67302 | 73.34194 | 0.0134464 | 0.0046020 |
East Cambridgeshire | 216 | 247 | 216 | 8216 | 20939 | 29155 | 41.75094 | 0.0043745 | 0.0012342 |
Fenland | 179 | 265 | 179 | 10010 | 16271 | 26281 | 41.16076 | 0.0024054 | 0.0013423 |
Huntingdonshire | 310 | 302 | 310 | 20270 | 31621 | 51891 | 102.90672 | 0.0132382 | 0.0023001 |
South Cambridgeshire | 328 | 284 | 328 | 34916 | 39466 | 74382 | 98.77528 | 0.0143335 | 0.0042710 |
Allerdale | 188 | 203 | 188 | 6436 | 11733 | 18169 | 33.91827 | 0.0002556 | 0.0019898 |
Barrow-in-Furness | 144 | 173 | 144 | 5100 | 4715 | 9815 | 20.75604 | 0.0002271 | 0.0014106 |
Carlisle | 306 | 242 | 306 | 9904 | 5953 | 15857 | 78.20939 | 0.0005917 | 0.0021074 |
Copeland | 162 | 185 | 162 | 7919 | 5986 | 13905 | 26.13944 | 0.0001593 | 0.0017038 |
Eden | 225 | 187 | 225 | 6209 | 4666 | 10875 | 41.29631 | 0.0002394 | 0.0016928 |
South Lakeland | 234 | 235 | 234 | 9651 | 8994 | 18645 | 56.17406 | 0.0005490 | 0.0020873 |
Amber Valley | 281 | 271 | 281 | 21778 | 25962 | 47740 | 77.94638 | 0.0014457 | 0.0019987 |
Bolsover | 242 | 243 | 242 | 15315 | 20347 | 35662 | 54.66120 | 0.0006313 | 0.0014976 |
Chesterfield | 242 | 256 | 242 | 21349 | 17107 | 38456 | 56.87320 | 0.0007520 | 0.0017426 |
Derbyshire Dales | 201 | 251 | 201 | 13161 | 11828 | 24989 | 42.88387 | 0.0009256 | 0.0013577 |
Erewash | 200 | 275 | 200 | 16623 | 28395 | 45018 | 50.97433 | 0.0012799 | 0.0017058 |
High Peak | 188 | 255 | 188 | 7663 | 17319 | 24982 | 45.93415 | 0.0008832 | 0.0009999 |
North East Derbyshire | 172 | 274 | 172 | 13414 | 28664 | 42078 | 42.70590 | 0.0007958 | 0.0014644 |
South Derbyshire | 216 | 276 | 216 | 14306 | 28077 | 42383 | 53.41385 | 0.0011521 | 0.0016710 |
East Devon | 315 | 261 | 315 | 12430 | 18130 | 30560 | 83.85873 | 0.0015576 | 0.0029037 |
Exeter | 248 | 241 | 248 | 37151 | 10809 | 47960 | 57.60331 | 0.0011451 | 0.0047422 |
Mid Devon | 163 | 220 | 163 | 5569 | 13667 | 19236 | 31.82063 | 0.0007052 | 0.0015827 |
North Devon | 261 | 233 | 261 | 7735 | 4645 | 12380 | 56.35792 | 0.0007480 | 0.0012730 |
South Hams | 282 | 235 | 282 | 16938 | 13322 | 30260 | 65.87841 | 0.0012274 | 0.0025189 |
Teignbridge | 232 | 252 | 232 | 12250 | 20987 | 33237 | 58.11052 | 0.0010440 | 0.0023279 |
Torridge | 116 | 196 | 116 | 3575 | 8288 | 11863 | 14.07664 | 0.0003644 | 0.0009993 |
West Devon | 125 | 208 | 125 | 4593 | 8149 | 12742 | 22.82693 | 0.0005090 | 0.0009780 |
Christchurch | 175 | 192 | 175 | 10677 | 10213 | 20890 | 24.36314 | 0.0012017 | 0.0012651 |
East Dorset | 197 | 234 | 197 | 13531 | 19487 | 33018 | 37.02858 | 0.0023127 | 0.0016371 |
North Dorset | 254 | 216 | 254 | 6962 | 9997 | 16959 | 47.73131 | 0.0018001 | 0.0011060 |
Purbeck | 226 | 186 | 226 | 7634 | 8732 | 16366 | 33.64330 | 0.0010481 | 0.0011865 |
West Dorset | 235 | 238 | 235 | 18059 | 11425 | 29484 | 49.90794 | 0.0017699 | 0.0020121 |
Weymouth and Portland | 206 | 209 | 206 | 3447 | 11981 | 15428 | 35.60819 | 0.0005798 | 0.0008754 |
Eastbourne | 204 | 227 | 204 | 12373 | 12830 | 25203 | 36.12422 | 0.0054015 | 0.0010266 |
Hastings | 164 | 236 | 164 | 8006 | 11732 | 19738 | 29.94627 | 0.0049038 | 0.0009044 |
Lewes | 202 | 224 | 202 | 14403 | 19800 | 34203 | 34.92845 | 0.0104541 | 0.0011926 |
Rother | 182 | 215 | 182 | 9630 | 15054 | 24684 | 27.26210 | 0.0074697 | 0.0010183 |
Wealden | 258 | 261 | 258 | 14989 | 30274 | 45263 | 58.96939 | 0.0186274 | 0.0013393 |
Basildon | 321 | 282 | 321 | 36071 | 36057 | 72128 | 92.09181 | 0.0612035 | 0.0019214 |
Braintree | 270 | 277 | 270 | 15184 | 31582 | 46766 | 74.27107 | 0.0271398 | 0.0013120 |
Brentwood | 289 | 223 | 289 | 17745 | 19995 | 37740 | 52.37953 | 0.0409946 | 0.0012340 |
Castle Point | 154 | 236 | 154 | 7467 | 23473 | 30940 | 28.09746 | 0.0251378 | 0.0007424 |
Chelmsford | 293 | 275 | 293 | 30575 | 34222 | 64797 | 83.33582 | 0.0512377 | 0.0018830 |
Colchester | 327 | 270 | 327 | 22968 | 24545 | 47513 | 94.70758 | 0.0235711 | 0.0016488 |
Epping Forest | 290 | 251 | 290 | 21509 | 35475 | 56984 | 68.68786 | 0.0711352 | 0.0015571 |
Harlow | 294 | 232 | 294 | 15994 | 16492 | 32486 | 57.74732 | 0.0195485 | 0.0013293 |
Maldon | 210 | 210 | 210 | 6513 | 13689 | 20202 | 33.49157 | 0.0119064 | 0.0007505 |
Rochford | 178 | 239 | 178 | 10411 | 24351 | 34762 | 35.41168 | 0.0271557 | 0.0008385 |
Tendring | 229 | 257 | 229 | 6763 | 17203 | 23966 | 51.10530 | 0.0091833 | 0.0008516 |
Uttlesford | 307 | 240 | 307 | 17618 | 17973 | 35591 | 63.70076 | 0.0202609 | 0.0014814 |
Cheltenham | 293 | 272 | 293 | 24125 | 19592 | 43717 | 85.00521 | 0.0025958 | 0.0030665 |
Cotswold | 293 | 254 | 293 | 15685 | 13651 | 29336 | 71.25964 | 0.0041576 | 0.0018831 |
Forest of Dean | 206 | 248 | 206 | 6007 | 14512 | 20519 | 48.05798 | 0.0008705 | 0.0010042 |
Gloucester | 290 | 276 | 290 | 26099 | 23463 | 49562 | 85.55168 | 0.0014927 | 0.0030158 |
Stroud | 289 | 267 | 289 | 13241 | 20326 | 33567 | 83.56128 | 0.0024767 | 0.0018481 |
Tewkesbury | 322 | 249 | 322 | 25184 | 20469 | 45653 | 87.05614 | 0.0015420 | 0.0030289 |
Basingstoke and Deane | 338 | 280 | 338 | 25401 | 30492 | 55893 | 101.39306 | 0.0181075 | 0.0025112 |
East Hampshire | 328 | 268 | 328 | 15462 | 25476 | 40938 | 93.84842 | 0.0120776 | 0.0016435 |
Eastleigh | 309 | 260 | 309 | 32465 | 33798 | 66263 | 81.90592 | 0.0056096 | 0.0029667 |
Fareham | 310 | 264 | 310 | 24609 | 29734 | 54343 | 76.99256 | 0.0039958 | 0.0022174 |
Gosport | 272 | 237 | 272 | 7327 | 20473 | 27800 | 58.39117 | 0.0018505 | 0.0010068 |
Hart | 328 | 253 | 328 | 18470 | 26300 | 44770 | 78.77749 | 0.0156487 | 0.0018362 |
Havant | 211 | 248 | 211 | 17666 | 26401 | 44067 | 43.23830 | 0.0039611 | 0.0018958 |
New Forest | 302 | 279 | 302 | 22744 | 29791 | 52535 | 86.90241 | 0.0054670 | 0.0022859 |
Rushmoor | 334 | 258 | 334 | 25017 | 26056 | 51073 | 89.27181 | 0.0143124 | 0.0022710 |
Test Valley | 318 | 256 | 318 | 22956 | 24789 | 47745 | 79.16895 | 0.0075231 | 0.0021833 |
Winchester | 327 | 270 | 327 | 41929 | 23369 | 65298 | 89.55948 | 0.0114415 | 0.0035121 |
Broxbourne | 317 | 249 | 317 | 18151 | 25440 | 43591 | 73.49505 | 0.0391390 | 0.0015310 |
Dacorum | 338 | 286 | 338 | 23817 | 30858 | 54675 | 104.58269 | 0.0370314 | 0.0020320 |
East Hertfordshire | 297 | 274 | 297 | 22122 | 35988 | 58110 | 79.93959 | 0.0446914 | 0.0018916 |
Hertsmere | 316 | 242 | 316 | 25251 | 28231 | 53482 | 69.43996 | 0.0558631 | 0.0022121 |
North Hertfordshire | 293 | 273 | 293 | 20355 | 32707 | 53062 | 77.54596 | 0.0292122 | 0.0018191 |
St Albans | 318 | 271 | 318 | 26809 | 36418 | 63227 | 81.85818 | 0.0619411 | 0.0023555 |
Stevenage | 314 | 254 | 314 | 20748 | 18525 | 39273 | 72.02250 | 0.0171373 | 0.0017124 |
Three Rivers | 322 | 253 | 322 | 18584 | 27115 | 45699 | 76.96263 | 0.0380419 | 0.0018902 |
Watford | 332 | 248 | 332 | 28799 | 24774 | 53573 | 78.54169 | 0.0405963 | 0.0024651 |
Welwyn Hatfield | 336 | 271 | 336 | 38496 | 22907 | 61403 | 90.64350 | 0.0389517 | 0.0029540 |
Ashford | 255 | 254 | 255 | 15035 | 17786 | 32821 | 59.60893 | 0.0139988 | 0.0012927 |
Canterbury | 234 | 274 | 234 | 19479 | 18121 | 37600 | 61.96377 | 0.0115107 | 0.0014501 |
Dartford | 306 | 248 | 306 | 32588 | 27117 | 59705 | 69.01172 | 0.0545483 | 0.0016458 |
Dover | 234 | 249 | 234 | 9959 | 16669 | 26628 | 48.35895 | 0.0045037 | 0.0010274 |
Gravesham | 212 | 258 | 212 | 10155 | 25676 | 35831 | 42.33955 | 0.0298471 | 0.0008559 |
Maidstone | 296 | 278 | 296 | 29979 | 31058 | 61037 | 76.04405 | 0.0296875 | 0.0018485 |
Sevenoaks | 274 | 246 | 274 | 20929 | 30420 | 51349 | 58.51716 | 0.0566217 | 0.0013925 |
Shepway | 232 | 250 | 232 | 10992 | 14806 | 25798 | 48.02087 | 0.0065689 | 0.0010662 |
Swale | 237 | 274 | 237 | 12599 | 22875 | 35474 | 59.86629 | 0.0186895 | 0.0010335 |
Thanet | 188 | 242 | 188 | 5846 | 13348 | 19194 | 36.05674 | 0.0056380 | 0.0007948 |
Tonbridge and Malling | 270 | 254 | 270 | 30765 | 30473 | 61238 | 56.01878 | 0.0379614 | 0.0018185 |
Tunbridge Wells | 227 | 240 | 227 | 20116 | 22147 | 42263 | 47.12165 | 0.0336823 | 0.0014347 |
Burnley | 159 | 222 | 159 | 14595 | 15150 | 29745 | 33.54753 | 0.0003922 | 0.0016247 |
Chorley | 168 | 261 | 168 | 14994 | 26851 | 41845 | 43.70430 | 0.0007779 | 0.0016512 |
Fylde | 230 | 223 | 230 | 21711 | 13080 | 34791 | 52.67556 | 0.0005238 | 0.0027609 |
Hyndburn | 130 | 203 | 130 | 12702 | 17380 | 30082 | 20.42098 | 0.0002830 | 0.0015889 |
Lancaster | 209 | 274 | 209 | 8091 | 11592 | 19683 | 59.97534 | 0.0006400 | 0.0015040 |
Pendle | 178 | 212 | 178 | 10432 | 15013 | 25445 | 34.52029 | 0.0003655 | 0.0013588 |
Preston | 288 | 270 | 288 | 44352 | 21146 | 65498 | 84.42626 | 0.0011831 | 0.0042716 |
Ribble Valley | 187 | 190 | 187 | 14075 | 12870 | 26945 | 29.07366 | 0.0004309 | 0.0018088 |
Rossendale | 152 | 218 | 152 | 7571 | 16019 | 23590 | 28.52086 | 0.0004274 | 0.0010012 |
South Ribble | 233 | 256 | 233 | 23544 | 30099 | 53643 | 59.66094 | 0.0007475 | 0.0026508 |
West Lancashire | 214 | 266 | 214 | 19805 | 21733 | 41538 | 56.65700 | 0.0009294 | 0.0015818 |
Wyre | 157 | 226 | 157 | 10819 | 21156 | 31975 | 33.40469 | 0.0005131 | 0.0018022 |
Blaby | 304 | 264 | 304 | 31649 | 27848 | 59497 | 78.31709 | 0.0018932 | 0.0034461 |
Charnwood | 292 | 317 | 292 | 23040 | 34580 | 57620 | 107.91161 | 0.0024076 | 0.0026228 |
Harborough | 273 | 265 | 273 | 19547 | 21344 | 40891 | 64.82323 | 0.0026586 | 0.0022494 |
Hinckley and Bosworth | 256 | 283 | 256 | 15677 | 26835 | 42512 | 75.05241 | 0.0014834 | 0.0018541 |
Melton | 175 | 223 | 175 | 6142 | 10160 | 16302 | 26.91873 | 0.0009008 | 0.0009814 |
North West Leicestershire | 331 | 267 | 331 | 26666 | 19081 | 45747 | 95.63833 | 0.0013247 | 0.0024521 |
Oadby and Wigston | 162 | 215 | 162 | 11870 | 17102 | 28972 | 20.71941 | 0.0010987 | 0.0016922 |
Boston | 144 | 211 | 144 | 7495 | 7088 | 14583 | 23.15199 | 0.0004174 | 0.0010821 |
East Lindsey | 272 | 280 | 272 | 8351 | 12695 | 21046 | 85.42615 | 0.0007084 | 0.0012323 |
Lincoln | 229 | 261 | 229 | 25583 | 14947 | 40530 | 51.75565 | 0.0008666 | 0.0022827 |
North Kesteven | 308 | 295 | 308 | 16326 | 22631 | 38957 | 103.67317 | 0.0014144 | 0.0020627 |
South Holland | 212 | 265 | 212 | 8955 | 11472 | 20427 | 50.29864 | 0.0015531 | 0.0013288 |
South Kesteven | 275 | 303 | 275 | 14185 | 23275 | 37460 | 94.80642 | 0.0039822 | 0.0018098 |
West Lindsey | 180 | 265 | 180 | 9169 | 19863 | 29032 | 46.25926 | 0.0006861 | 0.0013060 |
Breckland | 246 | 281 | 246 | 12378 | 23016 | 35394 | 65.43999 | 0.0018253 | 0.0015886 |
Broadland | 181 | 251 | 181 | 18858 | 32823 | 51681 | 39.50570 | 0.0019036 | 0.0026217 |
Great Yarmouth | 198 | 220 | 198 | 9250 | 9511 | 18761 | 38.18528 | 0.0007335 | 0.0012681 |
King's Lynn and West Norfolk | 299 | 290 | 299 | 11047 | 14664 | 25711 | 94.66804 | 0.0025603 | 0.0013157 |
North Norfolk | 187 | 238 | 187 | 8506 | 11750 | 20256 | 34.85599 | 0.0013520 | 0.0011684 |
Norwich | 283 | 259 | 283 | 48392 | 21251 | 69643 | 63.73725 | 0.0026206 | 0.0041001 |
South Norfolk | 263 | 258 | 263 | 22671 | 28315 | 50986 | 60.76567 | 0.0026761 | 0.0027300 |
Corby | 202 | 239 | 202 | 9176 | 8734 | 17910 | 38.33096 | 0.0013677 | 0.0012179 |
Daventry | 269 | 284 | 269 | 17275 | 18078 | 35353 | 79.04507 | 0.0033339 | 0.0020310 |
East Northamptonshire | 244 | 274 | 244 | 10043 | 22265 | 32308 | 68.11886 | 0.0038892 | 0.0013554 |
Kettering | 268 | 284 | 268 | 13980 | 18491 | 32471 | 70.87864 | 0.0030991 | 0.0016957 |
Northampton | 337 | 307 | 337 | 39498 | 27141 | 66639 | 118.08045 | 0.0088677 | 0.0036166 |
South Northamptonshire | 289 | 293 | 289 | 13977 | 25354 | 39331 | 92.12130 | 0.0062021 | 0.0017508 |
Wellingborough | 318 | 262 | 318 | 14948 | 16857 | 31805 | 80.21191 | 0.0036900 | 0.0016290 |
Craven | 163 | 202 | 163 | 8901 | 9015 | 17916 | 30.47052 | 0.0005107 | 0.0011944 |
Hambleton | 275 | 248 | 275 | 17621 | 13906 | 31527 | 74.05896 | 0.0009081 | 0.0022288 |
Harrogate | 325 | 282 | 325 | 19366 | 18342 | 37708 | 110.93138 | 0.0023168 | 0.0024481 |
Richmondshire | 324 | 234 | 324 | 7255 | 7057 | 14312 | 93.34512 | 0.0007768 | 0.0011037 |
Ryedale | 168 | 188 | 168 | 7047 | 6445 | 13492 | 28.82552 | 0.0004876 | 0.0011190 |
Scarborough | 184 | 244 | 184 | 5058 | 6783 | 11841 | 46.02664 | 0.0005090 | 0.0008944 |
Selby | 213 | 264 | 213 | 13235 | 20848 | 34083 | 52.54992 | 0.0010276 | 0.0015011 |
Ashfield | 273 | 272 | 273 | 25763 | 27847 | 53610 | 76.99274 | 0.0010518 | 0.0022554 |
Bassetlaw | 251 | 280 | 251 | 16161 | 16975 | 33136 | 73.46786 | 0.0009655 | 0.0015236 |
Broxtowe | 251 | 280 | 251 | 18998 | 33183 | 52181 | 68.09294 | 0.0015889 | 0.0019933 |
Gedling | 178 | 275 | 178 | 15434 | 34039 | 49473 | 46.03025 | 0.0014039 | 0.0018589 |
Mansfield | 200 | 267 | 200 | 15911 | 23109 | 39020 | 47.93428 | 0.0008000 | 0.0015661 |
Newark and Sherwood | 226 | 288 | 226 | 17327 | 20763 | 38090 | 62.46194 | 0.0015555 | 0.0017440 |
Rushcliffe | 256 | 288 | 256 | 20897 | 30122 | 51019 | 76.63440 | 0.0020342 | 0.0022778 |
Cherwell | 332 | 298 | 332 | 23167 | 26000 | 49167 | 111.31845 | 0.0082417 | 0.0026410 |
Oxford | 333 | 287 | 333 | 45775 | 15693 | 61468 | 107.32489 | 0.0113616 | 0.0045709 |
South Oxfordshire | 337 | 268 | 337 | 23589 | 31775 | 55364 | 88.07716 | 0.0151645 | 0.0028817 |
Vale of White Horse | 336 | 272 | 336 | 24697 | 25427 | 50124 | 98.46835 | 0.0082747 | 0.0030820 |
West Oxfordshire | 333 | 260 | 333 | 11768 | 19990 | 31758 | 83.83685 | 0.0051550 | 0.0017197 |
Mendip | 250 | 247 | 250 | 11450 | 15842 | 27292 | 64.75602 | 0.0021761 | 0.0015764 |
Sedgemoor | 232 | 259 | 232 | 9209 | 16894 | 26103 | 60.36191 | 0.0010367 | 0.0015783 |
South Somerset | 321 | 277 | 321 | 15164 | 15892 | 31056 | 101.23392 | 0.0020952 | 0.0022205 |
Taunton Deane | 277 | 243 | 277 | 15713 | 9820 | 25533 | 66.05293 | 0.0012006 | 0.0022342 |
West Somerset | 165 | 153 | 165 | 2780 | 3167 | 5947 | 18.02491 | 0.0004053 | 0.0007693 |
Cannock Chase | 239 | 267 | 239 | 14864 | 23408 | 38272 | 57.70909 | 0.0009774 | 0.0013914 |
East Staffordshire | 294 | 291 | 294 | 23275 | 18822 | 42097 | 101.32347 | 0.0012667 | 0.0020181 |
Lichfield | 292 | 277 | 292 | 20396 | 24559 | 44955 | 84.24212 | 0.0020662 | 0.0019028 |
Newcastle-under-Lyme | 261 | 285 | 261 | 21455 | 29382 | 50837 | 79.24630 | 0.0011395 | 0.0019857 |
South Staffordshire | 240 | 290 | 240 | 17575 | 34347 | 51922 | 72.56398 | 0.0015476 | 0.0015857 |
Stafford | 314 | 294 | 314 | 23835 | 20934 | 44769 | 105.13228 | 0.0018028 | 0.0020109 |
Staffordshire Moorlands | 200 | 270 | 200 | 10201 | 22847 | 33048 | 49.71024 | 0.0007831 | 0.0011897 |
Tamworth | 272 | 268 | 272 | 11312 | 19185 | 30497 | 75.84114 | 0.0011977 | 0.0014167 |
Babergh | 237 | 243 | 237 | 11616 | 18040 | 29656 | 49.49746 | 0.0069612 | 0.0013146 |
Forest Heath | 224 | 206 | 224 | 13035 | 11543 | 24578 | 33.10973 | 0.0015872 | 0.0014177 |
Ipswich | 236 | 255 | 236 | 27497 | 21192 | 48689 | 53.76366 | 0.0057598 | 0.0023529 |
Mid Suffolk | 273 | 247 | 273 | 13930 | 20713 | 34643 | 63.35687 | 0.0042169 | 0.0016024 |
St Edmundsbury | 313 | 271 | 313 | 19511 | 17447 | 36958 | 88.32277 | 0.0039806 | 0.0018960 |
Suffolk Coastal | 285 | 239 | 285 | 15143 | 18880 | 34023 | 59.27719 | 0.0052585 | 0.0016880 |
Waveney | 193 | 239 | 193 | 8325 | 11675 | 20000 | 39.78191 | 0.0012538 | 0.0012324 |
Elmbridge | 305 | 245 | 305 | 27029 | 35122 | 62151 | 62.72055 | 0.0685952 | 0.0024269 |
Epsom and Ewell | 254 | 224 | 254 | 15227 | 22939 | 38166 | 43.36186 | 0.0395024 | 0.0013033 |
Guildford | 334 | 258 | 334 | 38372 | 30423 | 68795 | 85.17198 | 0.0361713 | 0.0030977 |
Mole Valley | 315 | 217 | 315 | 23768 | 19616 | 43384 | 53.14222 | 0.0298856 | 0.0020016 |
Reigate and Banstead | 333 | 262 | 333 | 32483 | 35696 | 68179 | 89.77510 | 0.0537983 | 0.0024743 |
Runnymede | 335 | 250 | 335 | 30604 | 21324 | 51928 | 82.53407 | 0.0279868 | 0.0027531 |
Spelthorne | 309 | 235 | 309 | 21043 | 30107 | 51150 | 57.35777 | 0.0369474 | 0.0021774 |
Surrey Heath | 328 | 243 | 328 | 23260 | 24154 | 47414 | 70.25703 | 0.0172171 | 0.0021745 |
Tandridge | 246 | 240 | 246 | 13937 | 22538 | 36475 | 59.01705 | 0.0367740 | 0.0011585 |
Waverley | 283 | 258 | 283 | 20886 | 27655 | 48541 | 68.70357 | 0.0272366 | 0.0019656 |
Woking | 321 | 232 | 321 | 20273 | 27207 | 47480 | 59.27815 | 0.0340234 | 0.0020659 |
North Warwickshire | 277 | 248 | 277 | 25282 | 16883 | 42165 | 58.55078 | 0.0017477 | 0.0024229 |
Nuneaton and Bedworth | 246 | 269 | 246 | 15037 | 29798 | 44835 | 52.50267 | 0.0019273 | 0.0018603 |
Rugby | 320 | 280 | 320 | 17523 | 20443 | 37966 | 101.36753 | 0.0031786 | 0.0020217 |
Stratford-on-Avon | 323 | 296 | 323 | 25409 | 22594 | 48003 | 113.24263 | 0.0043159 | 0.0028345 |
Warwick | 341 | 290 | 341 | 33726 | 25353 | 59079 | 112.36995 | 0.0056245 | 0.0035936 |
Adur | 179 | 194 | 179 | 9348 | 16454 | 25802 | 20.54255 | 0.0046602 | 0.0009409 |
Arun | 221 | 276 | 221 | 8962 | 27174 | 36136 | 58.30258 | 0.0058173 | 0.0010559 |
Chichester | 300 | 253 | 300 | 24254 | 16115 | 40369 | 73.41119 | 0.0088457 | 0.0017499 |
Crawley | 335 | 246 | 335 | 43108 | 18998 | 62106 | 72.56600 | 0.0248586 | 0.0029446 |
Horsham | 297 | 265 | 297 | 16707 | 26654 | 43361 | 75.17375 | 0.0180015 | 0.0015769 |
Mid Sussex | 306 | 263 | 306 | 20393 | 31709 | 52102 | 80.30516 | 0.0306906 | 0.0017534 |
Worthing | 218 | 236 | 218 | 16690 | 17756 | 34446 | 42.16681 | 0.0062165 | 0.0012322 |
Bromsgrove | 252 | 274 | 252 | 18870 | 25995 | 44865 | 66.89830 | 0.0023463 | 0.0020102 |
Malvern Hills | 199 | 255 | 199 | 10947 | 14054 | 25001 | 46.11698 | 0.0010464 | 0.0013943 |
Redditch | 262 | 259 | 262 | 13741 | 17512 | 31253 | 61.69639 | 0.0013303 | 0.0016096 |
Worcester | 277 | 269 | 277 | 21134 | 17845 | 38979 | 75.86830 | 0.0012321 | 0.0020818 |
Wychavon | 264 | 290 | 264 | 20602 | 24629 | 45231 | 83.46586 | 0.0017334 | 0.0021899 |
Wyre Forest | 168 | 266 | 168 | 8628 | 17456 | 26084 | 40.84484 | 0.0008476 | 0.0010503 |
Bolton | 291 | 302 | 291 | 33985 | 42018 | 76003 | 106.68833 | 0.0021221 | 0.0027325 |
Bury | 261 | 290 | 261 | 26895 | 41317 | 68212 | 83.76982 | 0.0021060 | 0.0024213 |
Manchester | 345 | 333 | 345 | 179517 | 72365 | 251882 | 161.42941 | 0.0081722 | 0.0134337 |
Oldham | 241 | 296 | 241 | 29113 | 36102 | 65215 | 80.47174 | 0.0019906 | 0.0025758 |
Rochdale | 258 | 286 | 258 | 25139 | 36507 | 61646 | 81.99142 | 0.0017133 | 0.0022337 |
Salford | 327 | 304 | 327 | 59144 | 51900 | 111044 | 118.37394 | 0.0039354 | 0.0053232 |
Stockport | 320 | 314 | 320 | 47968 | 58798 | 106766 | 127.30501 | 0.0044807 | 0.0047446 |
Tameside | 243 | 299 | 243 | 23571 | 45702 | 69273 | 84.14139 | 0.0023514 | 0.0023393 |
Trafford | 316 | 299 | 316 | 70188 | 50717 | 120905 | 113.06647 | 0.0048473 | 0.0068569 |
Wigan | 311 | 316 | 311 | 27578 | 59356 | 86934 | 126.87502 | 0.0023235 | 0.0024079 |
Knowsley | 221 | 273 | 221 | 30613 | 34820 | 65433 | 60.35691 | 0.0015454 | 0.0025930 |
Liverpool | 301 | 333 | 301 | 91162 | 50759 | 141921 | 130.03027 | 0.0042335 | 0.0055228 |
St. Helens | 259 | 283 | 259 | 22077 | 35479 | 57556 | 81.68252 | 0.0013260 | 0.0018928 |
Sefton | 217 | 316 | 217 | 28443 | 46950 | 75393 | 77.79284 | 0.0022610 | 0.0025645 |
Wirral | 241 | 324 | 241 | 17244 | 44072 | 61316 | 97.57457 | 0.0024890 | 0.0017127 |
Barnsley | 242 | 302 | 242 | 17314 | 37625 | 54939 | 78.98661 | 0.0015289 | 0.0016357 |
Doncaster | 291 | 314 | 291 | 26494 | 32298 | 58792 | 105.97681 | 0.0019361 | 0.0022314 |
Rotherham | 287 | 312 | 287 | 36886 | 43598 | 80484 | 110.48375 | 0.0018907 | 0.0027850 |
Sheffield | 337 | 337 | 337 | 63693 | 45426 | 109119 | 160.95208 | 0.0033646 | 0.0042047 |
Gateshead | 200 | 279 | 200 | 42942 | 42399 | 85341 | 51.61637 | 0.0017757 | 0.0035313 |
Newcastle upon Tyne | 320 | 292 | 320 | 89811 | 38300 | 128111 | 104.36164 | 0.0030717 | 0.0057526 |
North Tyneside | 256 | 283 | 256 | 32439 | 43079 | 75518 | 78.16212 | 0.0019184 | 0.0030158 |
South Tyneside | 149 | 271 | 149 | 14369 | 27022 | 41391 | 39.24558 | 0.0009407 | 0.0014669 |
Sunderland | 254 | 294 | 254 | 40830 | 34827 | 75657 | 81.87235 | 0.0018640 | 0.0028891 |
Birmingham | 345 | 343 | 345 | 166056 | 100223 | 266279 | 174.73617 | 0.0144646 | 0.0127334 |
Coventry | 339 | 321 | 339 | 50577 | 39493 | 90070 | 145.23539 | 0.0058079 | 0.0048386 |
Dudley | 318 | 318 | 318 | 38796 | 57172 | 95968 | 126.70449 | 0.0042945 | 0.0031201 |
Sandwell | 330 | 322 | 330 | 58716 | 61446 | 120162 | 138.97124 | 0.0058632 | 0.0045497 |
Solihull | 333 | 320 | 333 | 51374 | 49120 | 100494 | 133.30159 | 0.0075356 | 0.0053752 |
Walsall | 333 | 313 | 333 | 41782 | 48755 | 90537 | 130.19952 | 0.0039666 | 0.0033192 |
Wolverhampton | 314 | 305 | 314 | 44388 | 40094 | 84482 | 112.57007 | 0.0032852 | 0.0030924 |
Bradford | 337 | 318 | 337 | 50336 | 55040 | 105376 | 142.38026 | 0.0043787 | 0.0048884 |
Calderdale | 319 | 293 | 319 | 26978 | 28593 | 55571 | 123.10999 | 0.0019020 | 0.0022845 |
Kirklees | 318 | 323 | 318 | 34538 | 59527 | 94065 | 133.83505 | 0.0034612 | 0.0032210 |
Leeds | 340 | 340 | 340 | 121087 | 65369 | 186456 | 166.23405 | 0.0072535 | 0.0092803 |
Wakefield | 297 | 322 | 297 | 45101 | 45316 | 90417 | 120.17849 | 0.0029064 | 0.0038373 |
Barking and Dagenham | 259 | 278 | 259 | 28989 | 45584 | 74573 | 74.07906 | 0.0947743 | 0.0016538 |
Barnet | 335 | 295 | 335 | 53143 | 94328 | 147471 | 107.29323 | 0.2678205 | 0.0053627 |
Bexley | 297 | 282 | 297 | 28684 | 63899 | 92583 | 81.72835 | 0.1419983 | 0.0016966 |
Brent | 324 | 306 | 324 | 54353 | 86120 | 140473 | 115.73294 | 0.2552967 | 0.0066587 |
Bromley | 322 | 288 | 322 | 40897 | 80537 | 121434 | 104.05368 | 0.2233553 | 0.0022546 |
Camden | 345 | 282 | 345 | 227171 | 62784 | 289955 | 116.18251 | 0.4715192 | 0.0277070 |
Croydon | 306 | 302 | 306 | 39884 | 92094 | 131978 | 100.31073 | 0.2122394 | 0.0026456 |
Ealing | 342 | 296 | 342 | 63429 | 95217 | 158646 | 121.88623 | 0.2424303 | 0.0072984 |
Enfield | 314 | 294 | 314 | 41313 | 73140 | 114453 | 105.61314 | 0.1777036 | 0.0031087 |
Greenwich | 316 | 289 | 316 | 39593 | 70802 | 110395 | 97.80635 | 0.1959638 | 0.0024311 |
Hackney | 325 | 282 | 325 | 60542 | 75197 | 135739 | 104.27664 | 0.2704059 | 0.0068321 |
Hammersmith and Fulham | 340 | 273 | 340 | 90212 | 64765 | 154977 | 103.70858 | 0.3005236 | 0.0118080 |
Haringey | 300 | 286 | 300 | 37279 | 80177 | 117456 | 93.22087 | 0.2386431 | 0.0032502 |
Harrow | 311 | 287 | 311 | 28680 | 68538 | 97218 | 92.42766 | 0.1476876 | 0.0030209 |
Havering | 286 | 283 | 286 | 31769 | 59870 | 91639 | 80.88612 | 0.1240316 | 0.0018851 |
Hillingdon | 345 | 303 | 345 | 96119 | 61002 | 157121 | 123.20678 | 0.1448890 | 0.0086205 |
Hounslow | 339 | 298 | 339 | 73977 | 71624 | 145601 | 113.12328 | 0.1694069 | 0.0072375 |
Islington | 342 | 277 | 342 | 132028 | 70981 | 203009 | 102.43241 | 0.3661235 | 0.0151687 |
Kensington and Chelsea | 334 | 256 | 334 | 86860 | 50799 | 137659 | 87.89829 | 0.3011796 | 0.0144531 |
Kingston upon Thames | 317 | 272 | 317 | 35923 | 45101 | 81024 | 88.78187 | 0.1066740 | 0.0027264 |
Lambeth | 339 | 295 | 339 | 87037 | 115419 | 202456 | 120.60327 | 0.4329508 | 0.0086193 |
Lewisham | 273 | 288 | 273 | 32829 | 89663 | 122492 | 81.85742 | 0.2550396 | 0.0023540 |
Merton | 309 | 280 | 309 | 38381 | 67646 | 106027 | 87.42231 | 0.1894013 | 0.0028738 |
Newham | 331 | 305 | 331 | 49198 | 77274 | 126472 | 118.87240 | 0.2181891 | 0.0037221 |
Redbridge | 266 | 289 | 266 | 32064 | 77588 | 109652 | 80.78754 | 0.1798939 | 0.0020014 |
Richmond upon Thames | 316 | 273 | 316 | 38600 | 58964 | 97564 | 87.93170 | 0.1564364 | 0.0037355 |
Southwark | 343 | 297 | 343 | 132137 | 95381 | 227518 | 120.54708 | 0.4190788 | 0.0124909 |
Sutton | 323 | 268 | 323 | 29841 | 55030 | 84871 | 82.50370 | 0.1105433 | 0.0019988 |
Tower Hamlets | 340 | 296 | 340 | 185467 | 70808 | 256275 | 119.14147 | 0.4108055 | 0.0210011 |
Waltham Forest | 300 | 284 | 300 | 30367 | 71912 | 102279 | 87.15664 | 0.1866278 | 0.0023823 |
Wandsworth | 327 | 305 | 327 | 63894 | 124029 | 187923 | 121.44261 | 0.4178796 | 0.0058755 |
Westminster,City of London | 345 | 289 | 345 | 866007 | 42018 | 908025 | 109.10666 | 1.0000000 | 0.0736260 |
Isle of Anglesey | 156 | 203 | 156 | 3104 | 8796 | 11900 | 31.56061 | 0.0002621 | 0.0008721 |
Gwynedd | 198 | 256 | 198 | 11022 | 7125 | 18147 | 50.38462 | 0.0004746 | 0.0014136 |
Conwy | 144 | 244 | 144 | 7404 | 12011 | 19415 | 30.74925 | 0.0005230 | 0.0012531 |
Denbighshire | 168 | 231 | 168 | 11688 | 11327 | 23015 | 36.51620 | 0.0004665 | 0.0014354 |
Flintshire | 284 | 278 | 284 | 23770 | 25459 | 49229 | 87.62641 | 0.0012318 | 0.0021949 |
Wrexham | 263 | 264 | 263 | 13956 | 16546 | 30502 | 73.76438 | 0.0008075 | 0.0014989 |
Ceredigion | 119 | 211 | 119 | 4114 | 4008 | 8122 | 21.56446 | 0.0003086 | 0.0009089 |
Pembrokeshire | 242 | 245 | 242 | 4107 | 4992 | 9099 | 63.15133 | 0.0005744 | 0.0008883 |
Carmarthenshire | 169 | 269 | 169 | 10881 | 17404 | 28285 | 44.90724 | 0.0008303 | 0.0017942 |
Swansea | 279 | 300 | 279 | 27777 | 19589 | 47366 | 98.91703 | 0.0014553 | 0.0027418 |
Neath Port Talbot | 146 | 248 | 146 | 15691 | 22974 | 38665 | 32.14387 | 0.0006626 | 0.0020202 |
Bridgend | 192 | 261 | 192 | 17241 | 17783 | 35024 | 49.79841 | 0.0007512 | 0.0018916 |
The Vale of Glamorgan | 250 | 276 | 250 | 13263 | 26340 | 39603 | 77.19142 | 0.0014653 | 0.0018653 |
Cardiff | 321 | 310 | 321 | 73041 | 32252 | 105293 | 126.18715 | 0.0032443 | 0.0056728 |
Rhondda Cynon Taf | 239 | 289 | 239 | 19349 | 36305 | 55654 | 72.07335 | 0.0012933 | 0.0023061 |
Caerphilly | 244 | 278 | 244 | 15975 | 34600 | 50575 | 73.20084 | 0.0010057 | 0.0019126 |
Blaenau Gwent | 122 | 185 | 122 | 5439 | 11664 | 17103 | 18.05921 | 0.0002741 | 0.0008538 |
Torfaen | 149 | 222 | 149 | 13902 | 15181 | 29083 | 27.77521 | 0.0005208 | 0.0016802 |
Monmouthshire | 199 | 262 | 199 | 12988 | 17540 | 30528 | 50.15730 | 0.0012077 | 0.0015550 |
Newport | 251 | 264 | 251 | 30393 | 21238 | 51631 | 68.26980 | 0.0012649 | 0.0030589 |
Powys | 225 | 274 | 225 | 8116 | 11453 | 19569 | 63.48931 | 0.0009664 | 0.0011444 |
Merthyr Tydfil | 93 | 179 | 93 | 8549 | 8716 | 17265 | 14.11701 | 0.0003200 | 0.0010095 |
Question: Can you try to interpret these different centrality measures in the context of our data?
This is helpful, but we might also be interested in discussing the rankings: Which one is the most central local authority in the commuting network? Instead of reading from the table, we can just calculate the ranks.
To begin with, let’s do a test.
<- centralities %>%
test mutate(rank.test = dense_rank(desc(in.degree))) %>% # We are interested in dense ranking:
# i.e. two lines with the same value will
# have the same ranking.
# desc stands for descending order.
arrange(rank.test) %>% # Arranges the data frame based on rank.test.
glimpse()
Rows: 346
Columns: 11
$ names <chr> "Wiltshire", "Manchester", "Birmingham", "Camden", "Hilli…
$ in.degree <dbl> 345, 345, 345, 345, 345, 345, 344, 343, 343, 343, 342, 34…
$ out.degree <dbl> 331, 333, 343, 282, 303, 289, 307, 288, 312, 297, 315, 29…
$ degree <dbl> 345, 345, 345, 345, 345, 345, 344, 343, 343, 343, 342, 34…
$ w.in.degree <dbl> 39717, 179517, 166056, 227171, 96119, 866007, 44450, 4127…
$ w.out.degree <dbl> 55625, 72365, 100223, 62784, 61002, 42018, 27780, 27862, …
$ w.degree <dbl> 95342, 251882, 266279, 289955, 157121, 908025, 72230, 691…
$ btwnss <dbl> 160.51941, 161.42941, 174.73617, 116.18251, 123.20678, 10…
$ eigen <dbl> 0.015047862, 0.008172246, 0.014464632, 0.471519182, 0.144…
$ prank <dbl> 0.004065817, 0.013433702, 0.012733372, 0.027707044, 0.008…
$ rank.test <int> 1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, …
<- centralities %>%
ranks mutate_at(vars(in.degree:prank),
funs(dense_rank(desc(.)))) # . for all the selected variables
Warning: `funs()` was deprecated in dplyr 0.8.0.
ℹ Please use a list of either functions or lambdas:
# Simple named list: list(mean = mean, median = median)
# Auto named with `tibble::lst()`: tibble::lst(mean, median)
# Using lambdas list(~ mean(., trim = .2), ~ median(., na.rm = TRUE))
# Adds a prefix r_ before each column name to indicate the ranks
colnames(ranks) <- paste("r", colnames(ranks), sep = "_")
Question: Can you quickly compare the ranks
with the cetrnalities
object based on the rankings?
head(centralities)
# A tibble: 6 × 10
names in.degree out.degree degree w.in.degree w.out.degree w.degree btwnss
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 Hartlepo… 111 231 111 8360 11261 19621 21.4
2 Middlesb… 214 250 214 30038 20664 50702 53.1
3 Redcar a… 118 242 118 12786 21904 34690 23.5
4 Stockton… 216 292 216 29986 29329 59315 65.9
5 Darlingt… 237 258 237 18445 15036 33481 63.6
6 Halton 275 274 275 23080 22981 46061 82.8
# ℹ 2 more variables: eigen <dbl>, prank <dbl>
head(ranks)
# A tibble: 6 × 10
r_names r_in.degree r_out.degree r_degree r_w.in.degree r_w.out.degree
<chr> <int> <int> <int> <int> <int>
1 Hartlepool 160 101 160 308 315
2 Middlesbrough 113 82 113 101 215
3 Redcar and Cle… 158 90 158 263 199
4 Stockton-on-Te… 112 40 112 102 132
5 Darlington 95 74 95 200 282
6 Halton 64 58 64 154 186
# ℹ 4 more variables: r_w.degree <int>, r_btwnss <int>, r_eigen <int>,
# r_prank <int>
# So, because both dataframes have the same structure and order we can just use
# cbind().
<- cbind(centralities, ranks) %>%
centralities arrange(w.in.degree) %>%
select(-r_names) %>%
glimpse()
Rows: 346
Columns: 19
$ names <chr> "Isle of Wight", "West Somerset", "Isle of Anglesey", "…
$ in.degree <dbl> 219, 165, 156, 206, 116, 242, 119, 125, 184, 144, 122, …
$ out.degree <dbl> 244, 153, 203, 209, 196, 245, 211, 208, 244, 173, 185, …
$ degree <dbl> 219, 165, 156, 206, 116, 242, 119, 125, 184, 144, 122, …
$ w.in.degree <dbl> 2083, 2780, 3104, 3447, 3575, 4107, 4114, 4593, 5058, 5…
$ w.out.degree <dbl> 4544, 3167, 8796, 11981, 8288, 4992, 4008, 8149, 6783, …
$ w.degree <dbl> 6627, 5947, 11900, 15428, 11863, 9099, 8122, 12742, 118…
$ btwnss <dbl> 44.65755, 18.02491, 31.56061, 35.60819, 14.07664, 63.15…
$ eigen <dbl> 0.0019493428, 0.0004052957, 0.0002620964, 0.0005797550,…
$ prank <dbl> 0.0006276137, 0.0007693002, 0.0008720594, 0.0008753942,…
$ r_in.degree <int> 109, 142, 148, 119, 159, 91, 157, 155, 132, 153, 156, 1…
$ r_out.degree <int> 88, 131, 119, 116, 121, 87, 114, 117, 88, 130, 128, 108…
$ r_degree <int> 109, 142, 148, 119, 159, 91, 157, 155, 132, 153, 156, 1…
$ r_w.in.degree <int> 346, 345, 344, 343, 342, 341, 340, 339, 338, 337, 336, …
$ r_w.out.degree <int> 343, 345, 325, 302, 329, 339, 344, 330, 334, 340, 308, …
$ r_w.degree <int> 345, 346, 338, 330, 339, 343, 344, 336, 340, 342, 325, …
$ r_btwnss <int> 285, 344, 321, 308, 346, 218, 337, 336, 281, 339, 343, …
$ r_eigen <int> 207, 333, 342, 316, 337, 317, 339, 324, 325, 345, 341, …
$ r_prank <int> 346, 343, 337, 336, 328, 335, 332, 330, 334, 272, 339, …
# It combines the centralities (centralities) and ranks (ranks) objects by columns.
# You can imagine it as stacking the columns of ranks after the columns of centralities.
# Since both objects refer to the same observations (i.e. the same rows), we can
# just combine them.
# And this is a nicer table of centralities:
%>% kable(caption = "Centralities") %>%
centralities scroll_box(width = "100%", height = "300px") #Again the `kableExtra` function
names | in.degree | out.degree | degree | w.in.degree | w.out.degree | w.degree | btwnss | eigen | prank | r_in.degree | r_out.degree | r_degree | r_w.in.degree | r_w.out.degree | r_w.degree | r_btwnss | r_eigen | r_prank |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Isle of Wight | 219 | 244 | 219 | 2083 | 4544 | 6627 | 44.65755 | 0.0019493 | 0.0006276 | 109 | 88 | 109 | 346 | 343 | 345 | 285 | 207 | 346 |
West Somerset | 165 | 153 | 165 | 2780 | 3167 | 5947 | 18.02491 | 0.0004053 | 0.0007693 | 142 | 131 | 142 | 345 | 345 | 346 | 344 | 333 | 343 |
Isle of Anglesey | 156 | 203 | 156 | 3104 | 8796 | 11900 | 31.56061 | 0.0002621 | 0.0008721 | 148 | 119 | 148 | 344 | 325 | 338 | 321 | 342 | 337 |
Weymouth and Portland | 206 | 209 | 206 | 3447 | 11981 | 15428 | 35.60819 | 0.0005798 | 0.0008754 | 119 | 116 | 119 | 343 | 302 | 330 | 308 | 316 | 336 |
Torridge | 116 | 196 | 116 | 3575 | 8288 | 11863 | 14.07664 | 0.0003644 | 0.0009993 | 159 | 121 | 159 | 342 | 329 | 339 | 346 | 337 | 328 |
Pembrokeshire | 242 | 245 | 242 | 4107 | 4992 | 9099 | 63.15133 | 0.0005744 | 0.0008883 | 91 | 87 | 91 | 341 | 339 | 343 | 218 | 317 | 335 |
Ceredigion | 119 | 211 | 119 | 4114 | 4008 | 8122 | 21.56446 | 0.0003086 | 0.0009089 | 157 | 114 | 157 | 340 | 344 | 344 | 337 | 339 | 332 |
West Devon | 125 | 208 | 125 | 4593 | 8149 | 12742 | 22.82693 | 0.0005090 | 0.0009780 | 155 | 117 | 155 | 339 | 330 | 336 | 336 | 324 | 330 |
Scarborough | 184 | 244 | 184 | 5058 | 6783 | 11841 | 46.02664 | 0.0005090 | 0.0008944 | 132 | 88 | 132 | 338 | 334 | 340 | 281 | 325 | 334 |
Barrow-in-Furness | 144 | 173 | 144 | 5100 | 4715 | 9815 | 20.75604 | 0.0002271 | 0.0014106 | 153 | 130 | 153 | 337 | 340 | 342 | 339 | 345 | 272 |
Blaenau Gwent | 122 | 185 | 122 | 5439 | 11664 | 17103 | 18.05921 | 0.0002741 | 0.0008538 | 156 | 128 | 156 | 336 | 308 | 325 | 343 | 341 | 339 |
Mid Devon | 163 | 220 | 163 | 5569 | 13667 | 19236 | 31.82063 | 0.0007052 | 0.0015827 | 144 | 108 | 144 | 335 | 291 | 316 | 320 | 306 | 246 |
Thanet | 188 | 242 | 188 | 5846 | 13348 | 19194 | 36.05674 | 0.0056380 | 0.0007948 | 130 | 90 | 130 | 334 | 294 | 317 | 307 | 134 | 342 |
Forest of Dean | 206 | 248 | 206 | 6007 | 14512 | 20519 | 48.05798 | 0.0008705 | 0.0010042 | 119 | 84 | 119 | 333 | 287 | 306 | 271 | 287 | 324 |
Melton | 175 | 223 | 175 | 6142 | 10160 | 16302 | 26.91873 | 0.0009008 | 0.0009814 | 138 | 106 | 138 | 332 | 319 | 328 | 331 | 285 | 329 |
Eden | 225 | 187 | 225 | 6209 | 4666 | 10875 | 41.29631 | 0.0002394 | 0.0016928 | 105 | 126 | 105 | 331 | 341 | 341 | 295 | 344 | 225 |
Allerdale | 188 | 203 | 188 | 6436 | 11733 | 18169 | 33.91827 | 0.0002556 | 0.0019898 | 130 | 119 | 130 | 330 | 305 | 320 | 313 | 343 | 182 |
Maldon | 210 | 210 | 210 | 6513 | 13689 | 20202 | 33.49157 | 0.0119064 | 0.0007505 | 117 | 115 | 117 | 329 | 290 | 309 | 316 | 104 | 344 |
Tendring | 229 | 257 | 229 | 6763 | 17203 | 23966 | 51.10530 | 0.0091833 | 0.0008516 | 102 | 75 | 102 | 328 | 260 | 299 | 261 | 109 | 340 |
Rutland | 223 | 225 | 223 | 6776 | 6446 | 13222 | 40.36699 | 0.0012338 | 0.0010011 | 107 | 104 | 107 | 327 | 335 | 335 | 298 | 257 | 326 |
North Dorset | 254 | 216 | 254 | 6962 | 9997 | 16959 | 47.73131 | 0.0018001 | 0.0011060 | 80 | 111 | 80 | 326 | 320 | 326 | 274 | 221 | 311 |
Ryedale | 168 | 188 | 168 | 7047 | 6445 | 13492 | 28.82552 | 0.0004876 | 0.0011190 | 141 | 125 | 141 | 325 | 336 | 334 | 326 | 326 | 310 |
Richmondshire | 324 | 234 | 324 | 7255 | 7057 | 14312 | 93.34512 | 0.0007768 | 0.0011037 | 21 | 98 | 21 | 324 | 333 | 332 | 105 | 296 | 312 |
Gosport | 272 | 237 | 272 | 7327 | 20473 | 27800 | 58.39117 | 0.0018505 | 0.0010068 | 67 | 95 | 67 | 323 | 216 | 280 | 236 | 218 | 323 |
Conwy | 144 | 244 | 144 | 7404 | 12011 | 19415 | 30.74925 | 0.0005230 | 0.0012531 | 153 | 88 | 153 | 322 | 301 | 315 | 322 | 320 | 295 |
Castle Point | 154 | 236 | 154 | 7467 | 23473 | 30940 | 28.09746 | 0.0251378 | 0.0007424 | 149 | 96 | 149 | 321 | 179 | 262 | 328 | 77 | 345 |
Boston | 144 | 211 | 144 | 7495 | 7088 | 14583 | 23.15199 | 0.0004174 | 0.0010821 | 153 | 114 | 153 | 320 | 332 | 331 | 335 | 332 | 314 |
Rossendale | 152 | 218 | 152 | 7571 | 16019 | 23590 | 28.52086 | 0.0004274 | 0.0010012 | 150 | 109 | 150 | 319 | 274 | 300 | 327 | 331 | 325 |
Purbeck | 226 | 186 | 226 | 7634 | 8732 | 16366 | 33.64330 | 0.0010481 | 0.0011865 | 104 | 127 | 104 | 318 | 327 | 327 | 314 | 272 | 306 |
High Peak | 188 | 255 | 188 | 7663 | 17319 | 24982 | 45.93415 | 0.0008832 | 0.0009999 | 130 | 77 | 130 | 317 | 259 | 295 | 282 | 286 | 327 |
North Devon | 261 | 233 | 261 | 7735 | 4645 | 12380 | 56.35792 | 0.0007480 | 0.0012730 | 75 | 99 | 75 | 316 | 342 | 337 | 246 | 301 | 292 |
Copeland | 162 | 185 | 162 | 7919 | 5986 | 13905 | 26.13944 | 0.0001593 | 0.0017038 | 145 | 128 | 145 | 315 | 337 | 333 | 332 | 346 | 222 |
Hastings | 164 | 236 | 164 | 8006 | 11732 | 19738 | 29.94627 | 0.0049038 | 0.0009044 | 143 | 96 | 143 | 314 | 306 | 311 | 324 | 142 | 333 |
Lancaster | 209 | 274 | 209 | 8091 | 11592 | 19683 | 59.97534 | 0.0006400 | 0.0015040 | 118 | 58 | 118 | 313 | 309 | 312 | 226 | 312 | 259 |
Powys | 225 | 274 | 225 | 8116 | 11453 | 19569 | 63.48931 | 0.0009664 | 0.0011444 | 105 | 58 | 105 | 312 | 312 | 314 | 216 | 279 | 309 |
East Cambridgeshire | 216 | 247 | 216 | 8216 | 20939 | 29155 | 41.75094 | 0.0043745 | 0.0012342 | 112 | 85 | 112 | 311 | 210 | 275 | 294 | 151 | 296 |
Waveney | 193 | 239 | 193 | 8325 | 11675 | 20000 | 39.78191 | 0.0012538 | 0.0012324 | 127 | 93 | 127 | 310 | 307 | 310 | 299 | 255 | 298 |
East Lindsey | 272 | 280 | 272 | 8351 | 12695 | 21046 | 85.42615 | 0.0007084 | 0.0012323 | 67 | 52 | 67 | 309 | 300 | 304 | 128 | 305 | 299 |
Hartlepool | 111 | 231 | 111 | 8360 | 11261 | 19621 | 21.38152 | 0.0003901 | 0.0010887 | 160 | 101 | 160 | 308 | 315 | 313 | 338 | 335 | 313 |
North Norfolk | 187 | 238 | 187 | 8506 | 11750 | 20256 | 34.85599 | 0.0013520 | 0.0011684 | 131 | 94 | 131 | 307 | 304 | 308 | 311 | 246 | 307 |
Merthyr Tydfil | 93 | 179 | 93 | 8549 | 8716 | 17265 | 14.11701 | 0.0003200 | 0.0010095 | 161 | 129 | 161 | 306 | 328 | 324 | 345 | 338 | 322 |
Torbay | 191 | 252 | 191 | 8569 | 12764 | 21333 | 46.76698 | 0.0007531 | 0.0015136 | 129 | 80 | 129 | 305 | 299 | 303 | 276 | 298 | 257 |
Wyre Forest | 168 | 266 | 168 | 8628 | 17456 | 26084 | 40.84484 | 0.0008476 | 0.0010503 | 141 | 66 | 141 | 304 | 255 | 286 | 297 | 289 | 317 |
Craven | 163 | 202 | 163 | 8901 | 9015 | 17916 | 30.47052 | 0.0005107 | 0.0011944 | 144 | 120 | 144 | 303 | 323 | 322 | 323 | 323 | 303 |
South Holland | 212 | 265 | 212 | 8955 | 11472 | 20427 | 50.29864 | 0.0015531 | 0.0013288 | 115 | 67 | 115 | 302 | 311 | 307 | 264 | 233 | 285 |
Arun | 221 | 276 | 221 | 8962 | 27174 | 36136 | 58.30258 | 0.0058173 | 0.0010559 | 108 | 56 | 108 | 301 | 146 | 229 | 237 | 131 | 316 |
West Lindsey | 180 | 265 | 180 | 9169 | 19863 | 29032 | 46.25926 | 0.0006861 | 0.0013060 | 135 | 67 | 135 | 300 | 225 | 277 | 277 | 308 | 289 |
Corby | 202 | 239 | 202 | 9176 | 8734 | 17910 | 38.33096 | 0.0013677 | 0.0012179 | 121 | 93 | 121 | 299 | 326 | 323 | 302 | 245 | 301 |
Sedgemoor | 232 | 259 | 232 | 9209 | 16894 | 26103 | 60.36191 | 0.0010367 | 0.0015783 | 100 | 73 | 100 | 298 | 264 | 285 | 224 | 275 | 248 |
Great Yarmouth | 198 | 220 | 198 | 9250 | 9511 | 18761 | 38.18528 | 0.0007335 | 0.0012681 | 125 | 108 | 125 | 297 | 322 | 318 | 303 | 303 | 293 |
Adur | 179 | 194 | 179 | 9348 | 16454 | 25802 | 20.54255 | 0.0046602 | 0.0009409 | 136 | 122 | 136 | 296 | 270 | 287 | 341 | 144 | 331 |
Rother | 182 | 215 | 182 | 9630 | 15054 | 24684 | 27.26210 | 0.0074697 | 0.0010183 | 133 | 112 | 133 | 295 | 281 | 296 | 330 | 119 | 321 |
South Lakeland | 234 | 235 | 234 | 9651 | 8994 | 18645 | 56.17406 | 0.0005490 | 0.0020873 | 98 | 97 | 98 | 294 | 324 | 319 | 247 | 318 | 163 |
Carlisle | 306 | 242 | 306 | 9904 | 5953 | 15857 | 78.20939 | 0.0005917 | 0.0021074 | 39 | 90 | 39 | 293 | 338 | 329 | 165 | 314 | 162 |
Dover | 234 | 249 | 234 | 9959 | 16669 | 26628 | 48.35895 | 0.0045037 | 0.0010274 | 98 | 83 | 98 | 292 | 267 | 283 | 270 | 147 | 319 |
Fenland | 179 | 265 | 179 | 10010 | 16271 | 26281 | 41.16076 | 0.0024054 | 0.0013423 | 136 | 67 | 136 | 291 | 271 | 284 | 296 | 191 | 281 |
East Northamptonshire | 244 | 274 | 244 | 10043 | 22265 | 32308 | 68.11886 | 0.0038892 | 0.0013554 | 89 | 58 | 89 | 290 | 197 | 255 | 203 | 164 | 279 |
Gravesham | 212 | 258 | 212 | 10155 | 25676 | 35831 | 42.33955 | 0.0298471 | 0.0008559 | 115 | 74 | 115 | 289 | 161 | 231 | 292 | 67 | 338 |
Staffordshire Moorlands | 200 | 270 | 200 | 10201 | 22847 | 33048 | 49.71024 | 0.0007831 | 0.0011897 | 123 | 62 | 123 | 288 | 191 | 250 | 268 | 294 | 305 |
Rochford | 178 | 239 | 178 | 10411 | 24351 | 34762 | 35.41168 | 0.0271557 | 0.0008385 | 137 | 93 | 137 | 287 | 175 | 239 | 309 | 73 | 341 |
Pendle | 178 | 212 | 178 | 10432 | 15013 | 25445 | 34.52029 | 0.0003655 | 0.0013588 | 137 | 113 | 137 | 286 | 283 | 291 | 312 | 336 | 277 |
Christchurch | 175 | 192 | 175 | 10677 | 10213 | 20890 | 24.36314 | 0.0012017 | 0.0012651 | 138 | 123 | 138 | 285 | 318 | 305 | 333 | 262 | 294 |
Herefordshire, County of | 306 | 292 | 306 | 10786 | 13434 | 24220 | 103.12522 | 0.0019351 | 0.0013338 | 39 | 40 | 39 | 284 | 293 | 298 | 82 | 209 | 283 |
Wyre | 157 | 226 | 157 | 10819 | 21156 | 31975 | 33.40469 | 0.0005131 | 0.0018022 | 147 | 103 | 147 | 283 | 206 | 256 | 317 | 322 | 210 |
Carmarthenshire | 169 | 269 | 169 | 10881 | 17404 | 28285 | 44.90724 | 0.0008303 | 0.0017942 | 140 | 63 | 140 | 282 | 257 | 279 | 283 | 290 | 211 |
Malvern Hills | 199 | 255 | 199 | 10947 | 14054 | 25001 | 46.11698 | 0.0010464 | 0.0013943 | 124 | 77 | 124 | 281 | 288 | 293 | 279 | 273 | 273 |
Shepway | 232 | 250 | 232 | 10992 | 14806 | 25798 | 48.02087 | 0.0065689 | 0.0010662 | 100 | 82 | 100 | 280 | 285 | 288 | 272 | 125 | 315 |
Gwynedd | 198 | 256 | 198 | 11022 | 7125 | 18147 | 50.38462 | 0.0004746 | 0.0014136 | 125 | 76 | 125 | 279 | 331 | 321 | 263 | 327 | 271 |
King's Lynn and West Norfolk | 299 | 290 | 299 | 11047 | 14664 | 25711 | 94.66804 | 0.0025603 | 0.0013157 | 45 | 42 | 45 | 278 | 286 | 289 | 103 | 185 | 286 |
Cornwall,Isles of Scilly | 341 | 330 | 341 | 11163 | 18567 | 29730 | 155.46166 | 0.0032429 | 0.0016854 | 5 | 7 | 5 | 277 | 238 | 271 | 6 | 174 | 228 |
Tamworth | 272 | 268 | 272 | 11312 | 19185 | 30497 | 75.84114 | 0.0011977 | 0.0014167 | 67 | 64 | 67 | 276 | 232 | 266 | 177 | 264 | 270 |
Mendip | 250 | 247 | 250 | 11450 | 15842 | 27292 | 64.75602 | 0.0021761 | 0.0015764 | 84 | 85 | 84 | 275 | 276 | 281 | 212 | 199 | 250 |
North East Lincolnshire | 219 | 286 | 219 | 11562 | 10600 | 22162 | 65.06108 | 0.0007256 | 0.0013687 | 109 | 46 | 109 | 274 | 317 | 302 | 210 | 304 | 276 |
Babergh | 237 | 243 | 237 | 11616 | 18040 | 29656 | 49.49746 | 0.0069612 | 0.0013146 | 95 | 89 | 95 | 273 | 246 | 272 | 269 | 122 | 287 |
Denbighshire | 168 | 231 | 168 | 11688 | 11327 | 23015 | 36.51620 | 0.0004665 | 0.0014354 | 141 | 101 | 141 | 272 | 314 | 301 | 305 | 328 | 267 |
West Oxfordshire | 333 | 260 | 333 | 11768 | 19990 | 31758 | 83.83685 | 0.0051550 | 0.0017197 | 13 | 72 | 13 | 271 | 224 | 258 | 136 | 140 | 218 |
Oadby and Wigston | 162 | 215 | 162 | 11870 | 17102 | 28972 | 20.71941 | 0.0010987 | 0.0016922 | 145 | 112 | 145 | 270 | 262 | 278 | 340 | 270 | 226 |
Teignbridge | 232 | 252 | 232 | 12250 | 20987 | 33237 | 58.11052 | 0.0010440 | 0.0023279 | 100 | 80 | 100 | 269 | 209 | 248 | 238 | 274 | 136 |
Eastbourne | 204 | 227 | 204 | 12373 | 12830 | 25203 | 36.12422 | 0.0054015 | 0.0010266 | 120 | 102 | 120 | 268 | 298 | 292 | 306 | 138 | 320 |
Breckland | 246 | 281 | 246 | 12378 | 23016 | 35394 | 65.43999 | 0.0018253 | 0.0015886 | 88 | 51 | 88 | 267 | 185 | 235 | 209 | 219 | 244 |
East Devon | 315 | 261 | 315 | 12430 | 18130 | 30560 | 83.85873 | 0.0015576 | 0.0029037 | 30 | 71 | 30 | 266 | 243 | 263 | 135 | 231 | 87 |
Swale | 237 | 274 | 237 | 12599 | 22875 | 35474 | 59.86629 | 0.0186895 | 0.0010335 | 95 | 58 | 95 | 265 | 190 | 234 | 227 | 85 | 318 |
Hyndburn | 130 | 203 | 130 | 12702 | 17380 | 30082 | 20.42098 | 0.0002830 | 0.0015889 | 154 | 119 | 154 | 264 | 258 | 269 | 342 | 340 | 243 |
Redcar and Cleveland | 118 | 242 | 118 | 12786 | 21904 | 34690 | 23.46728 | 0.0004593 | 0.0017847 | 158 | 90 | 158 | 263 | 199 | 240 | 334 | 329 | 212 |
Monmouthshire | 199 | 262 | 199 | 12988 | 17540 | 30528 | 50.15730 | 0.0012077 | 0.0015550 | 124 | 70 | 124 | 262 | 253 | 264 | 265 | 261 | 254 |
Forest Heath | 224 | 206 | 224 | 13035 | 11543 | 24578 | 33.10973 | 0.0015872 | 0.0014177 | 106 | 118 | 106 | 261 | 310 | 297 | 318 | 228 | 269 |
Derbyshire Dales | 201 | 251 | 201 | 13161 | 11828 | 24989 | 42.88387 | 0.0009256 | 0.0013577 | 122 | 81 | 122 | 260 | 303 | 294 | 290 | 283 | 278 |
Selby | 213 | 264 | 213 | 13235 | 20848 | 34083 | 52.54992 | 0.0010276 | 0.0015011 | 114 | 68 | 114 | 259 | 212 | 244 | 256 | 276 | 260 |
Stroud | 289 | 267 | 289 | 13241 | 20326 | 33567 | 83.56128 | 0.0024767 | 0.0018481 | 53 | 65 | 53 | 258 | 221 | 246 | 138 | 188 | 202 |
The Vale of Glamorgan | 250 | 276 | 250 | 13263 | 26340 | 39603 | 77.19142 | 0.0014653 | 0.0018653 | 84 | 56 | 84 | 257 | 155 | 210 | 170 | 240 | 197 |
Chiltern | 253 | 234 | 253 | 13391 | 22558 | 35949 | 44.70020 | 0.0301093 | 0.0015106 | 81 | 98 | 81 | 256 | 194 | 230 | 284 | 65 | 258 |
North East Derbyshire | 172 | 274 | 172 | 13414 | 28664 | 42078 | 42.70590 | 0.0007958 | 0.0014644 | 139 | 58 | 139 | 255 | 133 | 200 | 291 | 293 | 265 |
East Dorset | 197 | 234 | 197 | 13531 | 19487 | 33018 | 37.02858 | 0.0023127 | 0.0016371 | 126 | 98 | 126 | 254 | 231 | 251 | 304 | 196 | 236 |
Redditch | 262 | 259 | 262 | 13741 | 17512 | 31253 | 61.69639 | 0.0013303 | 0.0016096 | 74 | 73 | 74 | 253 | 254 | 260 | 222 | 247 | 241 |
Torfaen | 149 | 222 | 149 | 13902 | 15181 | 29083 | 27.77521 | 0.0005208 | 0.0016802 | 151 | 107 | 151 | 252 | 279 | 276 | 329 | 321 | 229 |
Mid Suffolk | 273 | 247 | 273 | 13930 | 20713 | 34643 | 63.35687 | 0.0042169 | 0.0016024 | 66 | 85 | 66 | 251 | 214 | 241 | 217 | 155 | 242 |
Tandridge | 246 | 240 | 246 | 13937 | 22538 | 36475 | 59.01705 | 0.0367740 | 0.0011585 | 88 | 92 | 88 | 250 | 195 | 228 | 232 | 58 | 308 |
Wrexham | 263 | 264 | 263 | 13956 | 16546 | 30502 | 73.76438 | 0.0008075 | 0.0014989 | 73 | 68 | 73 | 249 | 268 | 265 | 184 | 291 | 261 |
South Northamptonshire | 289 | 293 | 289 | 13977 | 25354 | 39331 | 92.12130 | 0.0062021 | 0.0017508 | 53 | 39 | 53 | 248 | 166 | 211 | 108 | 128 | 214 |
Kettering | 268 | 284 | 268 | 13980 | 18491 | 32471 | 70.87864 | 0.0030991 | 0.0016957 | 70 | 48 | 70 | 247 | 240 | 254 | 196 | 176 | 224 |
Ribble Valley | 187 | 190 | 187 | 14075 | 12870 | 26945 | 29.07366 | 0.0004309 | 0.0018088 | 131 | 124 | 131 | 246 | 297 | 282 | 325 | 330 | 208 |
South Kesteven | 275 | 303 | 275 | 14185 | 23275 | 37460 | 94.80642 | 0.0039822 | 0.0018098 | 64 | 30 | 64 | 245 | 183 | 226 | 100 | 158 | 207 |
South Derbyshire | 216 | 276 | 216 | 14306 | 28077 | 42383 | 53.41385 | 0.0011521 | 0.0016710 | 112 | 56 | 112 | 244 | 138 | 196 | 252 | 266 | 230 |
South Tyneside | 149 | 271 | 149 | 14369 | 27022 | 41391 | 39.24558 | 0.0009407 | 0.0014669 | 151 | 61 | 151 | 243 | 150 | 204 | 301 | 281 | 264 |
Lewes | 202 | 224 | 202 | 14403 | 19800 | 34203 | 34.92845 | 0.0104541 | 0.0011926 | 121 | 105 | 121 | 242 | 226 | 243 | 310 | 108 | 304 |
Burnley | 159 | 222 | 159 | 14595 | 15150 | 29745 | 33.54753 | 0.0003922 | 0.0016247 | 146 | 107 | 146 | 241 | 280 | 270 | 315 | 334 | 239 |
North Lincolnshire | 249 | 297 | 249 | 14755 | 15493 | 30248 | 83.06742 | 0.0007716 | 0.0016239 | 85 | 35 | 85 | 240 | 278 | 268 | 141 | 297 | 240 |
Cannock Chase | 239 | 267 | 239 | 14864 | 23408 | 38272 | 57.70909 | 0.0009774 | 0.0013914 | 94 | 65 | 94 | 239 | 181 | 218 | 240 | 278 | 275 |
Wellingborough | 318 | 262 | 318 | 14948 | 16857 | 31805 | 80.21191 | 0.0036900 | 0.0016290 | 27 | 70 | 27 | 238 | 266 | 257 | 156 | 165 | 238 |
Wealden | 258 | 261 | 258 | 14989 | 30274 | 45263 | 58.96939 | 0.0186274 | 0.0013393 | 77 | 71 | 77 | 237 | 122 | 180 | 233 | 86 | 282 |
Chorley | 168 | 261 | 168 | 14994 | 26851 | 41845 | 43.70430 | 0.0007779 | 0.0016512 | 141 | 71 | 141 | 236 | 151 | 201 | 287 | 295 | 232 |
Ashford | 255 | 254 | 255 | 15035 | 17786 | 32821 | 59.60893 | 0.0139988 | 0.0012927 | 79 | 78 | 79 | 235 | 249 | 252 | 229 | 100 | 291 |
Nuneaton and Bedworth | 246 | 269 | 246 | 15037 | 29798 | 44835 | 52.50267 | 0.0019273 | 0.0018603 | 88 | 63 | 88 | 234 | 127 | 185 | 257 | 210 | 198 |
Suffolk Coastal | 285 | 239 | 285 | 15143 | 18880 | 34023 | 59.27719 | 0.0052585 | 0.0016880 | 57 | 93 | 57 | 233 | 236 | 245 | 231 | 139 | 227 |
South Somerset | 321 | 277 | 321 | 15164 | 15892 | 31056 | 101.23392 | 0.0020952 | 0.0022205 | 24 | 55 | 24 | 232 | 275 | 261 | 89 | 202 | 152 |
Braintree | 270 | 277 | 270 | 15184 | 31582 | 46766 | 74.27107 | 0.0271398 | 0.0013120 | 68 | 55 | 68 | 231 | 114 | 173 | 181 | 74 | 288 |
Epsom and Ewell | 254 | 224 | 254 | 15227 | 22939 | 38166 | 43.36186 | 0.0395024 | 0.0013033 | 80 | 105 | 80 | 230 | 188 | 219 | 288 | 48 | 290 |
Bolsover | 242 | 243 | 242 | 15315 | 20347 | 35662 | 54.66120 | 0.0006313 | 0.0014976 | 91 | 89 | 91 | 229 | 220 | 232 | 250 | 313 | 262 |
Gedling | 178 | 275 | 178 | 15434 | 34039 | 49473 | 46.03025 | 0.0014039 | 0.0018589 | 137 | 57 | 137 | 228 | 97 | 159 | 280 | 244 | 199 |
East Hampshire | 328 | 268 | 328 | 15462 | 25476 | 40938 | 93.84842 | 0.0120776 | 0.0016435 | 17 | 64 | 17 | 227 | 162 | 206 | 104 | 103 | 235 |
Hinckley and Bosworth | 256 | 283 | 256 | 15677 | 26835 | 42512 | 75.05241 | 0.0014834 | 0.0018541 | 78 | 49 | 78 | 226 | 152 | 195 | 179 | 239 | 200 |
Cotswold | 293 | 254 | 293 | 15685 | 13651 | 29336 | 71.25964 | 0.0041576 | 0.0018831 | 49 | 78 | 49 | 225 | 292 | 274 | 195 | 156 | 195 |
Neath Port Talbot | 146 | 248 | 146 | 15691 | 22974 | 38665 | 32.14387 | 0.0006626 | 0.0020202 | 152 | 84 | 152 | 224 | 187 | 216 | 319 | 311 | 171 |
Taunton Deane | 277 | 243 | 277 | 15713 | 9820 | 25533 | 66.05293 | 0.0012006 | 0.0022342 | 63 | 89 | 63 | 223 | 321 | 290 | 206 | 263 | 148 |
Mansfield | 200 | 267 | 200 | 15911 | 23109 | 39020 | 47.93428 | 0.0008000 | 0.0015661 | 123 | 65 | 123 | 222 | 184 | 213 | 273 | 292 | 252 |
Caerphilly | 244 | 278 | 244 | 15975 | 34600 | 50575 | 73.20084 | 0.0010057 | 0.0019126 | 89 | 54 | 89 | 221 | 91 | 155 | 189 | 277 | 186 |
Harlow | 294 | 232 | 294 | 15994 | 16492 | 32486 | 57.74732 | 0.0195485 | 0.0013293 | 48 | 100 | 48 | 220 | 269 | 253 | 239 | 84 | 284 |
Bassetlaw | 251 | 280 | 251 | 16161 | 16975 | 33136 | 73.46786 | 0.0009655 | 0.0015236 | 83 | 52 | 83 | 219 | 263 | 249 | 186 | 280 | 256 |
North Kesteven | 308 | 295 | 308 | 16326 | 22631 | 38957 | 103.67317 | 0.0014144 | 0.0020627 | 37 | 37 | 37 | 218 | 192 | 215 | 81 | 243 | 167 |
Erewash | 200 | 275 | 200 | 16623 | 28395 | 45018 | 50.97433 | 0.0012799 | 0.0017058 | 123 | 57 | 123 | 217 | 135 | 182 | 262 | 252 | 221 |
Worthing | 218 | 236 | 218 | 16690 | 17756 | 34446 | 42.16681 | 0.0062165 | 0.0012322 | 110 | 96 | 110 | 216 | 252 | 242 | 293 | 127 | 300 |
Horsham | 297 | 265 | 297 | 16707 | 26654 | 43361 | 75.17375 | 0.0180015 | 0.0015769 | 46 | 67 | 46 | 215 | 153 | 194 | 178 | 89 | 249 |
South Hams | 282 | 235 | 282 | 16938 | 13322 | 30260 | 65.87841 | 0.0012274 | 0.0025189 | 60 | 97 | 60 | 214 | 295 | 267 | 208 | 260 | 116 |
Bridgend | 192 | 261 | 192 | 17241 | 17783 | 35024 | 49.79841 | 0.0007512 | 0.0018916 | 128 | 71 | 128 | 213 | 250 | 237 | 267 | 300 | 192 |
Wirral | 241 | 324 | 241 | 17244 | 44072 | 61316 | 97.57457 | 0.0024890 | 0.0017127 | 92 | 10 | 92 | 212 | 59 | 107 | 98 | 187 | 219 |
Daventry | 269 | 284 | 269 | 17275 | 18078 | 35353 | 79.04507 | 0.0033339 | 0.0020310 | 69 | 48 | 69 | 211 | 245 | 236 | 160 | 171 | 169 |
Barnsley | 242 | 302 | 242 | 17314 | 37625 | 54939 | 78.98661 | 0.0015289 | 0.0016357 | 91 | 31 | 91 | 210 | 74 | 128 | 161 | 237 | 237 |
Newark and Sherwood | 226 | 288 | 226 | 17327 | 20763 | 38090 | 62.46194 | 0.0015555 | 0.0017440 | 104 | 44 | 104 | 209 | 213 | 220 | 220 | 232 | 216 |
Rugby | 320 | 280 | 320 | 17523 | 20443 | 37966 | 101.36753 | 0.0031786 | 0.0020217 | 25 | 52 | 25 | 208 | 218 | 221 | 87 | 175 | 170 |
South Staffordshire | 240 | 290 | 240 | 17575 | 34347 | 51922 | 72.56398 | 0.0015476 | 0.0015857 | 93 | 42 | 93 | 207 | 95 | 142 | 191 | 234 | 245 |
Uttlesford | 307 | 240 | 307 | 17618 | 17973 | 35591 | 63.70076 | 0.0202609 | 0.0014814 | 38 | 92 | 38 | 206 | 247 | 233 | 214 | 83 | 263 |
Hambleton | 275 | 248 | 275 | 17621 | 13906 | 31527 | 74.05896 | 0.0009081 | 0.0022288 | 64 | 84 | 64 | 205 | 289 | 259 | 183 | 284 | 151 |
Havant | 211 | 248 | 211 | 17666 | 26401 | 44067 | 43.23830 | 0.0039611 | 0.0018958 | 116 | 84 | 116 | 204 | 154 | 188 | 289 | 161 | 189 |
Brentwood | 289 | 223 | 289 | 17745 | 19995 | 37740 | 52.37953 | 0.0409946 | 0.0012340 | 53 | 106 | 53 | 203 | 223 | 222 | 258 | 46 | 297 |
West Dorset | 235 | 238 | 235 | 18059 | 11425 | 29484 | 49.90794 | 0.0017699 | 0.0020121 | 97 | 94 | 97 | 202 | 313 | 273 | 266 | 223 | 173 |
Broxbourne | 317 | 249 | 317 | 18151 | 25440 | 43591 | 73.49505 | 0.0391390 | 0.0015310 | 28 | 83 | 28 | 201 | 164 | 192 | 185 | 49 | 255 |
Darlington | 237 | 258 | 237 | 18445 | 15036 | 33481 | 63.64096 | 0.0007033 | 0.0018073 | 95 | 74 | 95 | 200 | 282 | 247 | 215 | 307 | 209 |
Hart | 328 | 253 | 328 | 18470 | 26300 | 44770 | 78.77749 | 0.0156487 | 0.0018362 | 17 | 79 | 17 | 199 | 156 | 186 | 162 | 93 | 203 |
Three Rivers | 322 | 253 | 322 | 18584 | 27115 | 45699 | 76.96263 | 0.0380419 | 0.0018902 | 23 | 79 | 23 | 198 | 149 | 178 | 173 | 52 | 193 |
North Somerset | 288 | 309 | 288 | 18813 | 32553 | 51366 | 106.51079 | 0.0033370 | 0.0024983 | 54 | 24 | 54 | 197 | 106 | 147 | 69 | 170 | 118 |
Broadland | 181 | 251 | 181 | 18858 | 32823 | 51681 | 39.50570 | 0.0019036 | 0.0026217 | 134 | 81 | 134 | 196 | 103 | 145 | 300 | 212 | 109 |
Bromsgrove | 252 | 274 | 252 | 18870 | 25995 | 44865 | 66.89830 | 0.0023463 | 0.0020102 | 82 | 58 | 82 | 195 | 159 | 184 | 205 | 193 | 176 |
Broxtowe | 251 | 280 | 251 | 18998 | 33183 | 52181 | 68.09294 | 0.0015889 | 0.0019933 | 83 | 52 | 83 | 194 | 101 | 139 | 204 | 227 | 181 |
Rhondda Cynon Taf | 239 | 289 | 239 | 19349 | 36305 | 55654 | 72.07335 | 0.0012933 | 0.0023061 | 94 | 43 | 94 | 193 | 78 | 125 | 193 | 251 | 138 |
Harrogate | 325 | 282 | 325 | 19366 | 18342 | 37708 | 110.93138 | 0.0023168 | 0.0024481 | 20 | 50 | 20 | 192 | 241 | 223 | 60 | 195 | 124 |
Canterbury | 234 | 274 | 234 | 19479 | 18121 | 37600 | 61.96377 | 0.0115107 | 0.0014501 | 98 | 58 | 98 | 191 | 244 | 225 | 221 | 105 | 266 |
St Edmundsbury | 313 | 271 | 313 | 19511 | 17447 | 36958 | 88.32277 | 0.0039806 | 0.0018960 | 32 | 61 | 32 | 190 | 256 | 227 | 117 | 159 | 188 |
Harborough | 273 | 265 | 273 | 19547 | 21344 | 40891 | 64.82323 | 0.0026586 | 0.0022494 | 66 | 67 | 66 | 189 | 201 | 207 | 211 | 182 | 147 |
West Lancashire | 214 | 266 | 214 | 19805 | 21733 | 41538 | 56.65700 | 0.0009294 | 0.0015818 | 113 | 66 | 113 | 188 | 200 | 203 | 245 | 282 | 247 |
Aylesbury Vale | 330 | 303 | 330 | 19831 | 34981 | 54812 | 113.28702 | 0.0227757 | 0.0020113 | 16 | 30 | 16 | 187 | 86 | 129 | 50 | 81 | 174 |
Blackpool | 178 | 246 | 178 | 19835 | 17775 | 37610 | 43.94347 | 0.0005901 | 0.0025846 | 137 | 86 | 137 | 186 | 251 | 224 | 286 | 315 | 112 |
Tunbridge Wells | 227 | 240 | 227 | 20116 | 22147 | 42263 | 47.12165 | 0.0336823 | 0.0014347 | 103 | 92 | 103 | 185 | 198 | 197 | 275 | 61 | 268 |
Huntingdonshire | 310 | 302 | 310 | 20270 | 31621 | 51891 | 102.90672 | 0.0132382 | 0.0023001 | 35 | 31 | 35 | 184 | 113 | 143 | 83 | 102 | 139 |
Woking | 321 | 232 | 321 | 20273 | 27207 | 47480 | 59.27815 | 0.0340234 | 0.0020659 | 24 | 100 | 24 | 183 | 145 | 170 | 230 | 60 | 165 |
North Hertfordshire | 293 | 273 | 293 | 20355 | 32707 | 53062 | 77.54596 | 0.0292122 | 0.0018191 | 49 | 59 | 49 | 182 | 105 | 137 | 169 | 70 | 204 |
Mid Sussex | 306 | 263 | 306 | 20393 | 31709 | 52102 | 80.30516 | 0.0306906 | 0.0017534 | 39 | 69 | 39 | 181 | 112 | 140 | 155 | 63 | 213 |
Lichfield | 292 | 277 | 292 | 20396 | 24559 | 44955 | 84.24212 | 0.0020662 | 0.0019028 | 50 | 55 | 50 | 180 | 172 | 183 | 133 | 203 | 187 |
Wychavon | 264 | 290 | 264 | 20602 | 24629 | 45231 | 83.46586 | 0.0017334 | 0.0021899 | 72 | 42 | 72 | 179 | 170 | 181 | 139 | 225 | 157 |
South Bucks | 310 | 223 | 310 | 20603 | 20381 | 40984 | 55.75605 | 0.0262182 | 0.0023714 | 35 | 106 | 35 | 178 | 219 | 205 | 249 | 75 | 131 |
Southend-on-Sea | 247 | 260 | 247 | 20661 | 29749 | 50410 | 57.62656 | 0.0460325 | 0.0012049 | 87 | 72 | 87 | 177 | 129 | 156 | 241 | 44 | 302 |
Stevenage | 314 | 254 | 314 | 20748 | 18525 | 39273 | 72.02250 | 0.0171373 | 0.0017124 | 31 | 78 | 31 | 176 | 239 | 212 | 194 | 91 | 220 |
Waverley | 283 | 258 | 283 | 20886 | 27655 | 48541 | 68.70357 | 0.0272366 | 0.0019656 | 59 | 74 | 59 | 175 | 144 | 163 | 200 | 72 | 184 |
Rushcliffe | 256 | 288 | 256 | 20897 | 30122 | 51019 | 76.63440 | 0.0020342 | 0.0022778 | 78 | 44 | 78 | 174 | 123 | 151 | 174 | 204 | 143 |
Sevenoaks | 274 | 246 | 274 | 20929 | 30420 | 51349 | 58.51716 | 0.0566217 | 0.0013925 | 65 | 86 | 65 | 173 | 121 | 148 | 235 | 38 | 274 |
Spelthorne | 309 | 235 | 309 | 21043 | 30107 | 51150 | 57.35777 | 0.0369474 | 0.0021774 | 36 | 97 | 36 | 172 | 124 | 149 | 243 | 57 | 159 |
Worcester | 277 | 269 | 277 | 21134 | 17845 | 38979 | 75.86830 | 0.0012321 | 0.0020818 | 63 | 63 | 63 | 171 | 248 | 214 | 176 | 258 | 164 |
Chesterfield | 242 | 256 | 242 | 21349 | 17107 | 38456 | 56.87320 | 0.0007520 | 0.0017426 | 91 | 76 | 91 | 170 | 261 | 217 | 244 | 299 | 217 |
Bedford | 314 | 297 | 314 | 21392 | 22483 | 43875 | 100.59431 | 0.0154519 | 0.0018139 | 31 | 35 | 31 | 169 | 196 | 189 | 90 | 94 | 206 |
Newcastle-under-Lyme | 261 | 285 | 261 | 21455 | 29382 | 50837 | 79.24630 | 0.0011395 | 0.0019857 | 75 | 47 | 75 | 168 | 131 | 153 | 158 | 268 | 183 |
Epping Forest | 290 | 251 | 290 | 21509 | 35475 | 56984 | 68.68786 | 0.0711352 | 0.0015571 | 52 | 81 | 52 | 167 | 84 | 121 | 201 | 33 | 253 |
Fylde | 230 | 223 | 230 | 21711 | 13080 | 34791 | 52.67556 | 0.0005238 | 0.0027609 | 101 | 106 | 101 | 166 | 296 | 238 | 255 | 319 | 96 |
Amber Valley | 281 | 271 | 281 | 21778 | 25962 | 47740 | 77.94638 | 0.0014457 | 0.0019987 | 61 | 61 | 61 | 165 | 160 | 168 | 167 | 242 | 180 |
Thurrock | 281 | 268 | 281 | 21804 | 34873 | 56677 | 75.03469 | 0.0589668 | 0.0013440 | 61 | 64 | 61 | 164 | 87 | 122 | 180 | 37 | 280 |
St. Helens | 259 | 283 | 259 | 22077 | 35479 | 57556 | 81.68252 | 0.0013260 | 0.0018928 | 76 | 49 | 76 | 163 | 83 | 120 | 151 | 248 | 190 |
East Hertfordshire | 297 | 274 | 297 | 22122 | 35988 | 58110 | 79.93959 | 0.0446914 | 0.0018916 | 46 | 58 | 46 | 162 | 81 | 118 | 157 | 45 | 191 |
Northumberland | 287 | 310 | 287 | 22254 | 43011 | 65265 | 105.96942 | 0.0024251 | 0.0023084 | 55 | 23 | 55 | 161 | 62 | 95 | 72 | 189 | 137 |
South Norfolk | 263 | 258 | 263 | 22671 | 28315 | 50986 | 60.76567 | 0.0026761 | 0.0027300 | 73 | 74 | 73 | 160 | 136 | 152 | 223 | 181 | 100 |
Medway | 308 | 312 | 308 | 22710 | 50453 | 73163 | 109.01019 | 0.0533814 | 0.0015706 | 37 | 21 | 37 | 159 | 50 | 75 | 64 | 42 | 251 |
New Forest | 302 | 279 | 302 | 22744 | 29791 | 52535 | 86.90241 | 0.0054670 | 0.0022859 | 42 | 53 | 42 | 158 | 128 | 138 | 126 | 137 | 140 |
Test Valley | 318 | 256 | 318 | 22956 | 24789 | 47745 | 79.16895 | 0.0075231 | 0.0021833 | 27 | 76 | 27 | 157 | 168 | 167 | 159 | 118 | 158 |
Colchester | 327 | 270 | 327 | 22968 | 24545 | 47513 | 94.70758 | 0.0235711 | 0.0016488 | 18 | 62 | 18 | 156 | 173 | 169 | 102 | 80 | 233 |
Charnwood | 292 | 317 | 292 | 23040 | 34580 | 57620 | 107.91161 | 0.0024076 | 0.0026228 | 50 | 16 | 50 | 155 | 92 | 119 | 65 | 190 | 108 |
Halton | 275 | 274 | 275 | 23080 | 22981 | 46061 | 82.81950 | 0.0012432 | 0.0021577 | 64 | 58 | 64 | 154 | 186 | 175 | 142 | 256 | 161 |
Cherwell | 332 | 298 | 332 | 23167 | 26000 | 49167 | 111.31845 | 0.0082417 | 0.0026410 | 14 | 34 | 14 | 153 | 158 | 161 | 59 | 114 | 107 |
Surrey Heath | 328 | 243 | 328 | 23260 | 24154 | 47414 | 70.25703 | 0.0172171 | 0.0021745 | 17 | 89 | 17 | 152 | 177 | 171 | 197 | 90 | 160 |
East Staffordshire | 294 | 291 | 294 | 23275 | 18822 | 42097 | 101.32347 | 0.0012667 | 0.0020181 | 48 | 41 | 48 | 151 | 237 | 199 | 88 | 253 | 172 |
Telford and Wrekin | 324 | 296 | 324 | 23376 | 18322 | 41698 | 109.90081 | 0.0018745 | 0.0020630 | 21 | 36 | 21 | 150 | 242 | 202 | 62 | 216 | 166 |
South Ribble | 233 | 256 | 233 | 23544 | 30099 | 53643 | 59.66094 | 0.0007475 | 0.0026508 | 99 | 76 | 99 | 149 | 125 | 132 | 228 | 302 | 105 |
Tameside | 243 | 299 | 243 | 23571 | 45702 | 69273 | 84.14139 | 0.0023514 | 0.0023393 | 90 | 33 | 90 | 148 | 54 | 82 | 134 | 192 | 135 |
South Oxfordshire | 337 | 268 | 337 | 23589 | 31775 | 55364 | 88.07716 | 0.0151645 | 0.0028817 | 9 | 64 | 9 | 147 | 110 | 127 | 118 | 95 | 89 |
Mole Valley | 315 | 217 | 315 | 23768 | 19616 | 43384 | 53.14222 | 0.0298856 | 0.0020016 | 30 | 110 | 30 | 146 | 228 | 193 | 253 | 66 | 177 |
Flintshire | 284 | 278 | 284 | 23770 | 25459 | 49229 | 87.62641 | 0.0012318 | 0.0021949 | 58 | 54 | 58 | 145 | 163 | 160 | 122 | 259 | 156 |
Dacorum | 338 | 286 | 338 | 23817 | 30858 | 54675 | 104.58269 | 0.0370314 | 0.0020320 | 8 | 46 | 8 | 144 | 117 | 130 | 75 | 56 | 168 |
Stafford | 314 | 294 | 314 | 23835 | 20934 | 44769 | 105.13228 | 0.0018028 | 0.0020109 | 31 | 38 | 31 | 143 | 211 | 187 | 74 | 220 | 175 |
Swindon | 334 | 293 | 334 | 23868 | 24439 | 48307 | 112.57493 | 0.0066072 | 0.0024599 | 12 | 39 | 12 | 142 | 174 | 164 | 55 | 124 | 122 |
Blackburn with Darwen | 204 | 245 | 204 | 23988 | 19666 | 43654 | 46.17387 | 0.0006750 | 0.0024693 | 120 | 87 | 120 | 141 | 227 | 191 | 278 | 310 | 120 |
Cheltenham | 293 | 272 | 293 | 24125 | 19592 | 43717 | 85.00521 | 0.0025958 | 0.0030665 | 49 | 60 | 49 | 140 | 229 | 190 | 130 | 184 | 75 |
Chichester | 300 | 253 | 300 | 24254 | 16115 | 40369 | 73.41119 | 0.0088457 | 0.0017499 | 44 | 79 | 44 | 139 | 272 | 209 | 187 | 111 | 215 |
Fareham | 310 | 264 | 310 | 24609 | 29734 | 54343 | 76.99256 | 0.0039958 | 0.0022174 | 35 | 68 | 35 | 138 | 130 | 131 | 172 | 157 | 153 |
Vale of White Horse | 336 | 272 | 336 | 24697 | 25427 | 50124 | 98.46835 | 0.0082747 | 0.0030820 | 10 | 60 | 10 | 137 | 165 | 157 | 96 | 113 | 74 |
Rushmoor | 334 | 258 | 334 | 25017 | 26056 | 51073 | 89.27181 | 0.0143124 | 0.0022710 | 12 | 74 | 12 | 136 | 157 | 150 | 114 | 99 | 144 |
Rochdale | 258 | 286 | 258 | 25139 | 36507 | 61646 | 81.99142 | 0.0017133 | 0.0022337 | 77 | 46 | 77 | 135 | 76 | 103 | 145 | 226 | 149 |
Tewkesbury | 322 | 249 | 322 | 25184 | 20469 | 45653 | 87.05614 | 0.0015420 | 0.0030289 | 23 | 83 | 23 | 134 | 217 | 179 | 125 | 236 | 77 |
Bournemouth | 248 | 283 | 248 | 25210 | 32998 | 58208 | 72.37210 | 0.0044016 | 0.0028426 | 86 | 49 | 86 | 133 | 102 | 117 | 192 | 149 | 92 |
Hertsmere | 316 | 242 | 316 | 25251 | 28231 | 53482 | 69.43996 | 0.0558631 | 0.0022121 | 29 | 90 | 29 | 132 | 137 | 135 | 198 | 39 | 154 |
North Warwickshire | 277 | 248 | 277 | 25282 | 16883 | 42165 | 58.55078 | 0.0017477 | 0.0024229 | 63 | 84 | 63 | 131 | 265 | 198 | 234 | 224 | 127 |
Basingstoke and Deane | 338 | 280 | 338 | 25401 | 30492 | 55893 | 101.39306 | 0.0181075 | 0.0025112 | 8 | 52 | 8 | 130 | 118 | 124 | 86 | 88 | 117 |
Stratford-on-Avon | 323 | 296 | 323 | 25409 | 22594 | 48003 | 113.24263 | 0.0043159 | 0.0028345 | 22 | 36 | 22 | 129 | 193 | 165 | 51 | 152 | 93 |
Lincoln | 229 | 261 | 229 | 25583 | 14947 | 40530 | 51.75565 | 0.0008666 | 0.0022827 | 102 | 71 | 102 | 128 | 284 | 208 | 259 | 288 | 142 |
York | 304 | 310 | 304 | 25651 | 21058 | 46709 | 117.86975 | 0.0023097 | 0.0026595 | 41 | 23 | 41 | 127 | 208 | 174 | 42 | 197 | 104 |
Ashfield | 273 | 272 | 273 | 25763 | 27847 | 53610 | 76.99274 | 0.0010518 | 0.0022554 | 66 | 60 | 66 | 126 | 142 | 133 | 171 | 271 | 145 |
Plymouth | 332 | 300 | 332 | 25793 | 20138 | 45931 | 124.45365 | 0.0015797 | 0.0032944 | 14 | 32 | 14 | 125 | 222 | 176 | 26 | 229 | 60 |
Gloucester | 290 | 276 | 290 | 26099 | 23463 | 49562 | 85.55168 | 0.0014927 | 0.0030158 | 52 | 56 | 52 | 124 | 180 | 158 | 127 | 238 | 79 |
Doncaster | 291 | 314 | 291 | 26494 | 32298 | 58792 | 105.97681 | 0.0019361 | 0.0022314 | 51 | 19 | 51 | 123 | 108 | 116 | 71 | 208 | 150 |
North West Leicestershire | 331 | 267 | 331 | 26666 | 19081 | 45747 | 95.63833 | 0.0013247 | 0.0024521 | 15 | 65 | 15 | 122 | 234 | 177 | 99 | 249 | 123 |
St Albans | 318 | 271 | 318 | 26809 | 36418 | 63227 | 81.85818 | 0.0619411 | 0.0023555 | 27 | 61 | 27 | 121 | 77 | 99 | 148 | 35 | 132 |
Bury | 261 | 290 | 261 | 26895 | 41317 | 68212 | 83.76982 | 0.0021060 | 0.0024213 | 75 | 42 | 75 | 120 | 66 | 86 | 137 | 201 | 128 |
Calderdale | 319 | 293 | 319 | 26978 | 28593 | 55571 | 123.10999 | 0.0019020 | 0.0022845 | 26 | 39 | 26 | 119 | 134 | 126 | 29 | 213 | 141 |
Elmbridge | 305 | 245 | 305 | 27029 | 35122 | 62151 | 62.72055 | 0.0685952 | 0.0024269 | 40 | 87 | 40 | 118 | 85 | 101 | 219 | 34 | 126 |
Wycombe | 339 | 283 | 339 | 27246 | 32323 | 59569 | 100.06675 | 0.0304376 | 0.0027075 | 7 | 49 | 7 | 117 | 107 | 111 | 92 | 64 | 102 |
Ipswich | 236 | 255 | 236 | 27497 | 21192 | 48689 | 53.76366 | 0.0057598 | 0.0023529 | 96 | 77 | 96 | 116 | 205 | 162 | 251 | 133 | 134 |
Wigan | 311 | 316 | 311 | 27578 | 59356 | 86934 | 126.87502 | 0.0023235 | 0.0024079 | 34 | 17 | 34 | 115 | 34 | 57 | 23 | 194 | 129 |
Swansea | 279 | 300 | 279 | 27777 | 19589 | 47366 | 98.91703 | 0.0014553 | 0.0027418 | 62 | 32 | 62 | 114 | 230 | 172 | 94 | 241 | 98 |
Sefton | 217 | 316 | 217 | 28443 | 46950 | 75393 | 77.79284 | 0.0022610 | 0.0025645 | 111 | 17 | 111 | 113 | 53 | 69 | 168 | 198 | 114 |
Bracknell Forest | 336 | 263 | 336 | 28503 | 31002 | 59505 | 84.64837 | 0.0181350 | 0.0026867 | 10 | 69 | 10 | 112 | 116 | 112 | 131 | 87 | 103 |
Harrow | 311 | 287 | 311 | 28680 | 68538 | 97218 | 92.42766 | 0.1476876 | 0.0030209 | 34 | 45 | 34 | 111 | 22 | 48 | 107 | 26 | 78 |
Bexley | 297 | 282 | 297 | 28684 | 63899 | 92583 | 81.72835 | 0.1419983 | 0.0016966 | 46 | 50 | 46 | 110 | 28 | 52 | 150 | 28 | 223 |
Watford | 332 | 248 | 332 | 28799 | 24774 | 53573 | 78.54169 | 0.0405963 | 0.0024651 | 14 | 84 | 14 | 109 | 169 | 134 | 163 | 47 | 121 |
Barking and Dagenham | 259 | 278 | 259 | 28989 | 45584 | 74573 | 74.07906 | 0.0947743 | 0.0016538 | 76 | 54 | 76 | 108 | 55 | 71 | 182 | 32 | 231 |
Shropshire | 336 | 330 | 336 | 29111 | 34424 | 63535 | 148.35300 | 0.0036140 | 0.0027990 | 10 | 7 | 10 | 107 | 94 | 98 | 8 | 166 | 94 |
Oldham | 241 | 296 | 241 | 29113 | 36102 | 65215 | 80.47174 | 0.0019906 | 0.0025758 | 92 | 36 | 92 | 106 | 79 | 96 | 154 | 206 | 113 |
Bath and North East Somerset | 318 | 289 | 318 | 29241 | 23945 | 53186 | 106.11349 | 0.0063148 | 0.0031748 | 27 | 43 | 27 | 105 | 178 | 136 | 70 | 126 | 67 |
Sutton | 323 | 268 | 323 | 29841 | 55030 | 84871 | 82.50370 | 0.1105433 | 0.0019988 | 22 | 64 | 22 | 104 | 40 | 59 | 144 | 30 | 179 |
Maidstone | 296 | 278 | 296 | 29979 | 31058 | 61037 | 76.04405 | 0.0296875 | 0.0018485 | 47 | 54 | 47 | 103 | 115 | 109 | 175 | 68 | 201 |
Stockton-on-Tees | 216 | 292 | 216 | 29986 | 29329 | 59315 | 65.89576 | 0.0010995 | 0.0031831 | 112 | 40 | 112 | 102 | 132 | 114 | 207 | 269 | 66 |
Middlesbrough | 214 | 250 | 214 | 30038 | 20664 | 50702 | 53.13953 | 0.0006790 | 0.0029637 | 113 | 82 | 113 | 101 | 215 | 154 | 254 | 309 | 82 |
East Riding of Yorkshire | 292 | 326 | 292 | 30194 | 54386 | 84580 | 120.56251 | 0.0020021 | 0.0031038 | 50 | 9 | 50 | 100 | 41 | 60 | 35 | 205 | 70 |
Waltham Forest | 300 | 284 | 300 | 30367 | 71912 | 102279 | 87.15664 | 0.1866278 | 0.0023823 | 44 | 48 | 44 | 99 | 17 | 43 | 124 | 21 | 130 |
Newport | 251 | 264 | 251 | 30393 | 21238 | 51631 | 68.26980 | 0.0012649 | 0.0030589 | 83 | 68 | 83 | 98 | 204 | 146 | 202 | 254 | 76 |
Chelmsford | 293 | 275 | 293 | 30575 | 34222 | 64797 | 83.33582 | 0.0512377 | 0.0018830 | 49 | 57 | 49 | 97 | 96 | 97 | 140 | 43 | 196 |
Runnymede | 335 | 250 | 335 | 30604 | 21324 | 51928 | 82.53407 | 0.0279868 | 0.0027531 | 11 | 82 | 11 | 96 | 202 | 141 | 143 | 71 | 97 |
Knowsley | 221 | 273 | 221 | 30613 | 34820 | 65433 | 60.35691 | 0.0015454 | 0.0025930 | 108 | 59 | 108 | 95 | 89 | 93 | 225 | 235 | 111 |
Wokingham | 340 | 269 | 340 | 30764 | 42810 | 73574 | 90.37405 | 0.0237476 | 0.0032668 | 6 | 63 | 6 | 94 | 63 | 74 | 111 | 79 | 62 |
Tonbridge and Malling | 270 | 254 | 270 | 30765 | 30473 | 61238 | 56.01878 | 0.0379614 | 0.0018185 | 68 | 78 | 68 | 93 | 119 | 108 | 248 | 54 | 205 |
Blaby | 304 | 264 | 304 | 31649 | 27848 | 59497 | 78.31709 | 0.0018932 | 0.0034461 | 41 | 68 | 41 | 92 | 141 | 113 | 164 | 214 | 56 |
Havering | 286 | 283 | 286 | 31769 | 59870 | 91639 | 80.88612 | 0.1240316 | 0.0018851 | 56 | 49 | 56 | 91 | 32 | 53 | 152 | 29 | 194 |
Brighton and Hove | 297 | 287 | 297 | 31879 | 36938 | 68817 | 88.44945 | 0.0325543 | 0.0022023 | 46 | 45 | 46 | 90 | 75 | 84 | 116 | 62 | 155 |
Poole | 314 | 276 | 314 | 32048 | 24563 | 56611 | 87.92048 | 0.0045316 | 0.0030996 | 31 | 56 | 31 | 89 | 171 | 123 | 120 | 146 | 71 |
Redbridge | 266 | 289 | 266 | 32064 | 77588 | 109652 | 80.78754 | 0.1798939 | 0.0020014 | 71 | 43 | 71 | 88 | 12 | 34 | 153 | 22 | 178 |
North Tyneside | 256 | 283 | 256 | 32439 | 43079 | 75518 | 78.16212 | 0.0019184 | 0.0030158 | 78 | 49 | 78 | 87 | 61 | 68 | 166 | 211 | 80 |
Eastleigh | 309 | 260 | 309 | 32465 | 33798 | 66263 | 81.90592 | 0.0056096 | 0.0029667 | 36 | 72 | 36 | 86 | 98 | 91 | 146 | 136 | 81 |
Central Bedfordshire | 343 | 312 | 343 | 32469 | 66131 | 98600 | 129.24999 | 0.0390917 | 0.0028629 | 3 | 21 | 3 | 85 | 24 | 46 | 21 | 50 | 91 |
Reigate and Banstead | 333 | 262 | 333 | 32483 | 35696 | 68179 | 89.77510 | 0.0537983 | 0.0024743 | 13 | 70 | 13 | 84 | 82 | 87 | 112 | 41 | 119 |
Peterborough | 337 | 294 | 337 | 32552 | 19136 | 51688 | 111.41706 | 0.0080528 | 0.0029620 | 9 | 38 | 9 | 83 | 233 | 144 | 58 | 116 | 83 |
Dartford | 306 | 248 | 306 | 32588 | 27117 | 59705 | 69.01172 | 0.0545483 | 0.0016458 | 39 | 84 | 39 | 82 | 148 | 110 | 199 | 40 | 234 |
Lewisham | 273 | 288 | 273 | 32829 | 89663 | 122492 | 81.85742 | 0.2550396 | 0.0023540 | 66 | 44 | 66 | 81 | 8 | 25 | 149 | 13 | 133 |
West Berkshire | 340 | 277 | 340 | 33558 | 28003 | 61561 | 103.72536 | 0.0157734 | 0.0033439 | 6 | 55 | 6 | 80 | 139 | 104 | 79 | 92 | 58 |
Warwick | 341 | 290 | 341 | 33726 | 25353 | 59079 | 112.36995 | 0.0056245 | 0.0035936 | 5 | 42 | 5 | 79 | 167 | 115 | 57 | 135 | 52 |
Bolton | 291 | 302 | 291 | 33985 | 42018 | 76003 | 106.68833 | 0.0021221 | 0.0027325 | 51 | 31 | 51 | 78 | 65 | 66 | 68 | 200 | 99 |
Luton | 341 | 293 | 341 | 34348 | 33348 | 67696 | 117.08185 | 0.0292726 | 0.0026121 | 5 | 39 | 5 | 77 | 100 | 88 | 43 | 69 | 110 |
Kirklees | 318 | 323 | 318 | 34538 | 59527 | 94065 | 133.83505 | 0.0034612 | 0.0032210 | 27 | 11 | 27 | 76 | 33 | 51 | 17 | 168 | 65 |
South Cambridgeshire | 328 | 284 | 328 | 34916 | 39466 | 74382 | 98.77528 | 0.0143335 | 0.0042710 | 17 | 48 | 17 | 75 | 71 | 72 | 95 | 98 | 38 |
County Durham | 316 | 328 | 316 | 35081 | 64602 | 99683 | 136.76168 | 0.0025184 | 0.0033631 | 29 | 8 | 29 | 74 | 27 | 45 | 15 | 186 | 57 |
Kingston upon Thames | 317 | 272 | 317 | 35923 | 45101 | 81024 | 88.78187 | 0.1066740 | 0.0027264 | 28 | 60 | 28 | 73 | 58 | 64 | 115 | 31 | 101 |
Basildon | 321 | 282 | 321 | 36071 | 36057 | 72128 | 92.09181 | 0.0612035 | 0.0019214 | 24 | 50 | 24 | 72 | 80 | 77 | 109 | 36 | 185 |
Rotherham | 287 | 312 | 287 | 36886 | 43598 | 80484 | 110.48375 | 0.0018907 | 0.0027850 | 55 | 21 | 55 | 71 | 60 | 65 | 61 | 215 | 95 |
Windsor and Maidenhead | 341 | 273 | 341 | 36971 | 34482 | 71453 | 99.72553 | 0.0372343 | 0.0038264 | 5 | 59 | 5 | 70 | 93 | 79 | 93 | 55 | 47 |
Exeter | 248 | 241 | 248 | 37151 | 10809 | 47960 | 57.60331 | 0.0011451 | 0.0047422 | 86 | 91 | 86 | 69 | 316 | 166 | 242 | 267 | 32 |
Haringey | 300 | 286 | 300 | 37279 | 80177 | 117456 | 93.22087 | 0.2386431 | 0.0032502 | 44 | 46 | 44 | 68 | 11 | 29 | 106 | 15 | 63 |
Guildford | 334 | 258 | 334 | 38372 | 30423 | 68795 | 85.17198 | 0.0361713 | 0.0030977 | 12 | 74 | 12 | 67 | 120 | 85 | 129 | 59 | 72 |
Merton | 309 | 280 | 309 | 38381 | 67646 | 106027 | 87.42231 | 0.1894013 | 0.0028738 | 36 | 52 | 36 | 66 | 23 | 38 | 123 | 20 | 90 |
Welwyn Hatfield | 336 | 271 | 336 | 38496 | 22907 | 61403 | 90.64350 | 0.0389517 | 0.0029540 | 10 | 61 | 10 | 65 | 189 | 106 | 110 | 51 | 84 |
Richmond upon Thames | 316 | 273 | 316 | 38600 | 58964 | 97564 | 87.93170 | 0.1564364 | 0.0037355 | 29 | 59 | 29 | 64 | 35 | 47 | 119 | 25 | 48 |
Kingston upon Hull, City of | 292 | 298 | 292 | 38602 | 24199 | 62801 | 102.14345 | 0.0012955 | 0.0025353 | 50 | 34 | 50 | 63 | 176 | 100 | 85 | 250 | 115 |
Dudley | 318 | 318 | 318 | 38796 | 57172 | 95968 | 126.70449 | 0.0042945 | 0.0031201 | 27 | 15 | 27 | 62 | 37 | 49 | 24 | 153 | 68 |
Slough | 335 | 271 | 335 | 39282 | 31753 | 71035 | 94.80244 | 0.0380361 | 0.0041691 | 11 | 61 | 11 | 61 | 111 | 80 | 101 | 53 | 40 |
Northampton | 337 | 307 | 337 | 39498 | 27141 | 66639 | 118.08045 | 0.0088677 | 0.0036166 | 9 | 26 | 9 | 60 | 147 | 90 | 41 | 110 | 51 |
Greenwich | 316 | 289 | 316 | 39593 | 70802 | 110395 | 97.80635 | 0.1959638 | 0.0024311 | 29 | 43 | 29 | 59 | 21 | 33 | 97 | 19 | 125 |
Wiltshire | 345 | 331 | 345 | 39717 | 55625 | 95342 | 160.51941 | 0.0150479 | 0.0040658 | 1 | 6 | 1 | 58 | 38 | 50 | 5 | 96 | 42 |
Croydon | 306 | 302 | 306 | 39884 | 92094 | 131978 | 100.31073 | 0.2122394 | 0.0026456 | 39 | 31 | 39 | 57 | 7 | 21 | 91 | 18 | 106 |
Stoke-on-Trent | 313 | 309 | 313 | 40031 | 33667 | 73698 | 114.84293 | 0.0015778 | 0.0029178 | 32 | 24 | 32 | 56 | 99 | 73 | 48 | 230 | 86 |
Sunderland | 254 | 294 | 254 | 40830 | 34827 | 75657 | 81.87235 | 0.0018640 | 0.0028891 | 80 | 38 | 80 | 55 | 88 | 67 | 147 | 217 | 88 |
Bromley | 322 | 288 | 322 | 40897 | 80537 | 121434 | 104.05368 | 0.2233553 | 0.0022546 | 23 | 44 | 23 | 54 | 10 | 26 | 78 | 16 | 146 |
Portsmouth | 343 | 288 | 343 | 41272 | 27862 | 69134 | 115.85177 | 0.0059324 | 0.0032274 | 3 | 44 | 3 | 53 | 140 | 83 | 45 | 129 | 64 |
Enfield | 314 | 294 | 314 | 41313 | 73140 | 114453 | 105.61314 | 0.1777036 | 0.0031087 | 31 | 38 | 31 | 52 | 15 | 30 | 73 | 23 | 69 |
Derby | 316 | 308 | 316 | 41670 | 29802 | 71472 | 113.83201 | 0.0029402 | 0.0032790 | 29 | 25 | 29 | 51 | 126 | 78 | 49 | 178 | 61 |
Walsall | 333 | 313 | 333 | 41782 | 48755 | 90537 | 130.19952 | 0.0039666 | 0.0033192 | 13 | 20 | 13 | 50 | 52 | 54 | 19 | 160 | 59 |
Southampton | 321 | 300 | 321 | 41891 | 41234 | 83125 | 115.21255 | 0.0069496 | 0.0036577 | 24 | 32 | 24 | 49 | 67 | 63 | 47 | 123 | 50 |
Winchester | 327 | 270 | 327 | 41929 | 23369 | 65298 | 89.55948 | 0.0114415 | 0.0035121 | 18 | 62 | 18 | 48 | 182 | 94 | 113 | 106 | 55 |
Reading | 332 | 289 | 332 | 42267 | 32715 | 74982 | 112.58266 | 0.0227425 | 0.0040357 | 14 | 43 | 14 | 47 | 104 | 70 | 54 | 82 | 43 |
Gateshead | 200 | 279 | 200 | 42942 | 42399 | 85341 | 51.61637 | 0.0017757 | 0.0035313 | 123 | 53 | 123 | 46 | 64 | 58 | 260 | 222 | 53 |
Crawley | 335 | 246 | 335 | 43108 | 18998 | 62106 | 72.56600 | 0.0248586 | 0.0029446 | 11 | 86 | 11 | 45 | 235 | 102 | 190 | 78 | 85 |
Preston | 288 | 270 | 288 | 44352 | 21146 | 65498 | 84.42626 | 0.0011831 | 0.0042716 | 54 | 62 | 54 | 44 | 207 | 92 | 132 | 265 | 37 |
Wolverhampton | 314 | 305 | 314 | 44388 | 40094 | 84482 | 112.57007 | 0.0032852 | 0.0030924 | 31 | 28 | 31 | 43 | 69 | 61 | 56 | 172 | 73 |
Milton Keynes | 344 | 307 | 344 | 44450 | 27780 | 72230 | 122.22514 | 0.0253813 | 0.0035232 | 2 | 26 | 2 | 42 | 143 | 76 | 30 | 76 | 54 |
Wakefield | 297 | 322 | 297 | 45101 | 45316 | 90417 | 120.17849 | 0.0029064 | 0.0038373 | 46 | 12 | 46 | 41 | 57 | 55 | 37 | 179 | 46 |
Oxford | 333 | 287 | 333 | 45775 | 15693 | 61468 | 107.32489 | 0.0113616 | 0.0045709 | 13 | 45 | 13 | 40 | 277 | 105 | 66 | 107 | 34 |
Stockport | 320 | 314 | 320 | 47968 | 58798 | 106766 | 127.30501 | 0.0044807 | 0.0047446 | 25 | 19 | 25 | 39 | 36 | 37 | 22 | 148 | 31 |
Norwich | 283 | 259 | 283 | 48392 | 21251 | 69643 | 63.73725 | 0.0026206 | 0.0041001 | 59 | 73 | 59 | 38 | 203 | 81 | 213 | 183 | 41 |
Warrington | 326 | 302 | 326 | 49172 | 34607 | 83779 | 124.18728 | 0.0028033 | 0.0038653 | 19 | 31 | 19 | 37 | 90 | 62 | 27 | 180 | 45 |
Newham | 331 | 305 | 331 | 49198 | 77274 | 126472 | 118.87240 | 0.2181891 | 0.0037221 | 15 | 28 | 15 | 36 | 13 | 24 | 39 | 17 | 49 |
Bradford | 337 | 318 | 337 | 50336 | 55040 | 105376 | 142.38026 | 0.0043787 | 0.0048884 | 9 | 15 | 9 | 35 | 39 | 39 | 12 | 150 | 29 |
Coventry | 339 | 321 | 339 | 50577 | 39493 | 90070 | 145.23539 | 0.0058079 | 0.0048386 | 7 | 13 | 7 | 34 | 70 | 56 | 10 | 132 | 30 |
Cheshire West and Chester | 323 | 324 | 323 | 50910 | 51970 | 102880 | 141.77478 | 0.0034742 | 0.0039760 | 22 | 10 | 22 | 33 | 44 | 42 | 13 | 167 | 44 |
Cambridge | 312 | 250 | 312 | 51240 | 16062 | 67302 | 73.34194 | 0.0134464 | 0.0046020 | 33 | 82 | 33 | 32 | 273 | 89 | 188 | 101 | 33 |
Solihull | 333 | 320 | 333 | 51374 | 49120 | 100494 | 133.30159 | 0.0075356 | 0.0053752 | 13 | 14 | 13 | 31 | 51 | 44 | 18 | 117 | 26 |
Barnet | 335 | 295 | 335 | 53143 | 94328 | 147471 | 107.29323 | 0.2678205 | 0.0053627 | 11 | 37 | 11 | 30 | 6 | 14 | 67 | 11 | 27 |
Cheshire East | 331 | 334 | 331 | 53260 | 51773 | 105033 | 153.00249 | 0.0049410 | 0.0044883 | 15 | 4 | 15 | 29 | 46 | 41 | 7 | 141 | 36 |
Brent | 324 | 306 | 324 | 54353 | 86120 | 140473 | 115.73294 | 0.2552967 | 0.0066587 | 21 | 27 | 21 | 28 | 9 | 17 | 46 | 12 | 19 |
Sandwell | 330 | 322 | 330 | 58716 | 61446 | 120162 | 138.97124 | 0.0058632 | 0.0045497 | 16 | 12 | 16 | 27 | 30 | 28 | 14 | 130 | 35 |
Salford | 327 | 304 | 327 | 59144 | 51900 | 111044 | 118.37394 | 0.0039354 | 0.0053232 | 18 | 29 | 18 | 26 | 45 | 32 | 40 | 162 | 28 |
South Gloucestershire | 342 | 315 | 342 | 59359 | 53569 | 112928 | 143.90381 | 0.0071708 | 0.0067618 | 4 | 18 | 4 | 25 | 43 | 31 | 11 | 121 | 18 |
Hackney | 325 | 282 | 325 | 60542 | 75197 | 135739 | 104.27664 | 0.2704059 | 0.0068321 | 20 | 50 | 20 | 24 | 14 | 19 | 77 | 10 | 17 |
Ealing | 342 | 296 | 342 | 63429 | 95217 | 158646 | 121.88623 | 0.2424303 | 0.0072984 | 4 | 36 | 4 | 23 | 5 | 11 | 32 | 14 | 14 |
Sheffield | 337 | 337 | 337 | 63693 | 45426 | 109119 | 160.95208 | 0.0033646 | 0.0042047 | 9 | 3 | 9 | 22 | 56 | 35 | 4 | 169 | 39 |
Wandsworth | 327 | 305 | 327 | 63894 | 124029 | 187923 | 121.44261 | 0.4178796 | 0.0058755 | 18 | 28 | 18 | 21 | 1 | 9 | 33 | 5 | 22 |
Leicester | 328 | 311 | 328 | 67191 | 41007 | 108198 | 121.94219 | 0.0045364 | 0.0060454 | 17 | 22 | 17 | 20 | 68 | 36 | 31 | 145 | 20 |
Trafford | 316 | 299 | 316 | 70188 | 50717 | 120905 | 113.06647 | 0.0048473 | 0.0068569 | 29 | 33 | 29 | 19 | 49 | 27 | 53 | 143 | 16 |
Cardiff | 321 | 310 | 321 | 73041 | 32252 | 105293 | 126.18715 | 0.0032443 | 0.0056728 | 24 | 23 | 24 | 18 | 109 | 40 | 25 | 173 | 24 |
Hounslow | 339 | 298 | 339 | 73977 | 71624 | 145601 | 113.12328 | 0.1694069 | 0.0072375 | 7 | 34 | 7 | 17 | 18 | 15 | 52 | 24 | 15 |
Bristol, City of | 338 | 324 | 338 | 80907 | 54120 | 135027 | 146.21380 | 0.0085801 | 0.0081482 | 8 | 10 | 8 | 16 | 42 | 20 | 9 | 112 | 13 |
Kensington and Chelsea | 334 | 256 | 334 | 86860 | 50799 | 137659 | 87.89829 | 0.3011796 | 0.0144531 | 12 | 76 | 12 | 15 | 47 | 18 | 121 | 8 | 5 |
Lambeth | 339 | 295 | 339 | 87037 | 115419 | 202456 | 120.60327 | 0.4329508 | 0.0086193 | 7 | 37 | 7 | 14 | 2 | 8 | 34 | 3 | 12 |
Nottingham | 336 | 315 | 336 | 89650 | 38180 | 127830 | 134.64542 | 0.0039334 | 0.0059435 | 10 | 18 | 10 | 13 | 73 | 23 | 16 | 163 | 21 |
Newcastle upon Tyne | 320 | 292 | 320 | 89811 | 38300 | 128111 | 104.36164 | 0.0030717 | 0.0057526 | 25 | 40 | 25 | 12 | 72 | 22 | 76 | 177 | 23 |
Hammersmith and Fulham | 340 | 273 | 340 | 90212 | 64765 | 154977 | 103.70858 | 0.3005236 | 0.0118080 | 6 | 59 | 6 | 11 | 26 | 13 | 80 | 9 | 9 |
Liverpool | 301 | 333 | 301 | 91162 | 50759 | 141921 | 130.03027 | 0.0042335 | 0.0055228 | 43 | 5 | 43 | 10 | 48 | 16 | 20 | 154 | 25 |
Hillingdon | 345 | 303 | 345 | 96119 | 61002 | 157121 | 123.20678 | 0.1448890 | 0.0086205 | 1 | 30 | 1 | 9 | 31 | 12 | 28 | 27 | 11 |
Leeds | 340 | 340 | 340 | 121087 | 65369 | 186456 | 166.23405 | 0.0072535 | 0.0092803 | 6 | 2 | 6 | 8 | 25 | 10 | 2 | 120 | 10 |
Islington | 342 | 277 | 342 | 132028 | 70981 | 203009 | 102.43241 | 0.3661235 | 0.0151687 | 4 | 55 | 4 | 7 | 19 | 7 | 84 | 7 | 4 |
Southwark | 343 | 297 | 343 | 132137 | 95381 | 227518 | 120.54708 | 0.4190788 | 0.0124909 | 3 | 35 | 3 | 6 | 4 | 6 | 36 | 4 | 8 |
Birmingham | 345 | 343 | 345 | 166056 | 100223 | 266279 | 174.73617 | 0.0144646 | 0.0127334 | 1 | 1 | 1 | 5 | 3 | 3 | 1 | 97 | 7 |
Manchester | 345 | 333 | 345 | 179517 | 72365 | 251882 | 161.42941 | 0.0081722 | 0.0134337 | 1 | 5 | 1 | 4 | 16 | 5 | 3 | 115 | 6 |
Tower Hamlets | 340 | 296 | 340 | 185467 | 70808 | 256275 | 119.14147 | 0.4108055 | 0.0210011 | 6 | 36 | 6 | 3 | 20 | 4 | 38 | 6 | 3 |
Camden | 345 | 282 | 345 | 227171 | 62784 | 289955 | 116.18251 | 0.4715192 | 0.0277070 | 1 | 50 | 1 | 2 | 29 | 2 | 44 | 2 | 2 |
Westminster,City of London | 345 | 289 | 345 | 866007 | 42018 | 908025 | 109.10666 | 1.0000000 | 0.0736260 | 1 | 43 | 1 | 1 | 65 | 1 | 63 | 1 | 1 |
Compare centralities
The below code provides a corregram of the different centrality measures.
<- cor(centralities[,c(2:10)])
cor.mat corrplot(cor.mat, type="upper")
Question: Discuss the differences between the different centrality measures in the context of the commuting network.
Community detection
To begin with, we need to convert our network to an undirected one, as the fast_greedy
algorithm we are using can only be applied to such networks.
<- as.undirected(net.all,
net.all.und mode=c("mutual"),
edge.attr.comb = igraph_opt("edge.attr.comb"))
<- cluster_fast_greedy(net.all.und)
communities.net.all
# This provides a summary of the community algorithm:
print(communities.net.all)
IGRAPH clustering fast greedy, groups: 11, mod: 0.69
+ groups:
$`1`
[1] "E41000033" "E41000034" "E41000035" "E41000098" "E41000100" "E41000101"
[7] "E41000102" "E41000104" "E41000106" "E41000107" "E41000127" "E41000130"
[13] "E41000137" "E41000138" "E41000139" "E41000140" "E41000141" "E41000142"
[19] "E41000143" "E41000144" "E41000145" "E41000146" "E41000147" "E41000148"
[25] "E41000228" "E41000229" "E41000231" "E41000232" "E41000233" "E41000234"
[31] "E41000236" "E41000293" "E41000294" "E41000295" "E41000296" "E41000297"
[37] "E41000298" "E41000299" "E41000300" "E41000301" "E41000302" "E41000303"
[43] "E41000304" "E41000305" "E41000306" "E41000307" "E41000308" "E41000309"
[49] "E41000310" "E41000311" "E41000312" "E41000313" "E41000314" "E41000315"
+ ... omitted several groups/vertices
# To see how many communities we have, run the below:
length(communities.net.all)
[1] 11
# And these are the community sizes:
sizes(communities.net.all)
Community sizes
1 2 3 4 5 6 7 8 9 10 11
63 46 29 31 16 47 27 14 29 22 22
# Now, let's create a new object with the community membership
#communities.net.all_membership <- membership(communities.net.all)
# And convert it to a data.frame
<- membership(communities.net.all) %>%
communities.net.all_membership %>% # we first need to unclass the object
unclass %>% # we convert it to a dataframe
as.data.frame rename(community = ".") %>% # rename the community column
rownames_to_column("cmlad11cd") %>% # we 'move' the rownames to a
# new column in order to do a merge below
left_join(la.names) %>% # and now we can merge it with the LA names
arrange(community) %>% # arrange based on the community membership
glimpse()
Rows: 346
Columns: 3
$ cmlad11cd <chr> "E41000033", "E41000034", "E41000035", "E41000098", "E410001…
$ community <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …
$ cmlad11nm <chr> "Southend-on-Sea", "Thurrock", "Medway", "Basildon", "Brentw…
# this is just a test to see if the `left_join` led to any NAs
sapply(communities.net.all_membership, function(x) sum(is.na(x)))
cmlad11cd community cmlad11nm
0 0 0
Let’s try now to map our output. We need the local authorities shape file we have already loaded.
# First we merge the `la` object with the community membership
<- merge(la, communities.net.all_membership, by = "cmlad11cd")
la # Please note that I used base R for the above. I could have easily used the dplyr
# equivalent. Which function would this be?
# just a check to see how the merge worked
sapply(la, function(x) sum(is.na(x)))
cmlad11cd OBJECTID cmlad11nm.x cmlad11nmw Shape__Area
0 0 0 0 0
Shape__Length GlobalID community cmlad11nm.y geometry
0 0 0 0 0
# And this is our map
ggplot(la, aes(fill = as.factor(community))) +
geom_sf() +
ggtitle("Communities using the 'fast and greedy' algorithm")
Question: What do you think about the output? Can we learn anything? Can you try different community algorithms? Check igraph’s manual and Javed et al (2018)
Network Visualisation
The below chunks of code offer some intro to plotting network data. Have a look to see how the code works.
plot(net.all, # the graph to be plotted
layout=layout.fruchterman.reingold, # the layout method. see the igraph documentation for details
main='My first graph in R', # specifies the title
vertex.label.dist=0.5, # puts the name labels slightly off the dots
vertex.frame.color='blue', # the colour of the border of the dots
vertex.label.color='black', # the colour of the name labels
vertex.label.font=2, # the font of the name labels
vertex.label=V(net.all)$id, # specifies the labels of the vertices. in this case the 'name' attribute is used
vertex.label.cex=.5, # specifies the size of the font of the labels. can also be made to vary
edge.arrow.size=0.1) # specifies the arrow size
Not a very nice outcome :( Let’s remove some information
plot(net.all, # the graph to be plotted
layout=layout.fruchterman.reingold, # the layout method. see the igraph documentation for details
main='My second graph in R', # specifies the title
vertex.frame.color='blue', # the colour of the border of the dots
vertex.label.font=2, # the font of the name labels
vertex.label=NA, # no labels for the vertices
edge.arrow.size=0, # specifies the arrow size
vertex.size=5) # vertex size
Let’s try to only plot nodes with high weighted degree centrality.
# The below gives us the 90th percentile:
<- quantile(strength(net.all), .9)
q
# Then, we create a network with the nodes we DON'T want to plot. In this case the lowest 90%
<- V(net.all)[strength(net.all) < q] # 108659 is the 90% percentile. Feel free to play with different numbers
low_nodes
# And this is the network with the 10% of the most central nodes
<- delete.vertices(net.all, low_nodes) net.all.central
Warning: `delete.vertices()` was deprecated in igraph 2.0.0.
ℹ Please use `delete_vertices()` instead.
# The below uses the node degree centrality to plot the node size.
# Pay attention to the 0.0001 factor.
plot(net.all.central, # the graph to be plotted
layout=layout.fruchterman.reingold, # the layout method. see the igraph documentation for details
main='My third graph in R', # specifies the title
vertex.frame.color='blue', # the colour of the border of the dots
vertex.label.font=2, # the font of the name labels
vertex.label=V(net.all.central)$id, # no labels for the vertices
vertex.label.font=1, # the font type of the name labels (1 plain, 2 bold, 3, italic, 4 bold italic, 5 symbol)
vertex.label.cex=.5, # specifies the size of the font of the labels. can also be made to vary
edge.arrow.size=0, # specifies the arrow size
vertex.size=strength(net.all.central)*0.0001) # defines the node size based on weighted degree centrality
Not very nice either…
For the next time:
-
spend some time browsing the
igraph
’s manual, -
search for code online to
plot large netwoks in R using igraph
, and -
use the following tutorials
in order to produce more meaningful network visualisations of the UK commuting network.
I am interesting in one or multiple plots with:
-
all or a subset of the nodes and edges. How could you select such a subset?
-
the communities you detected.
-
varying size of nodes based on a centrality measure. Again, you can decide to plot a subset of the network based on some network characteristics.
-
an appropriate to the network layout.
Mapping
Until now we focused mostly on the topology of the network and we ignored its spatial dimension. However, this is an important attribute of the commuting network and we should necessarily consider it and incorporate it in our analysis. To begin with we will map these commuting flows. Bare in mind that this is not a trivial process as, in essence, we need to attach the geographical coordinates to the network nodes and plot the network based on these coordinates. Given the size of our network this might be computationally expensive. It is also challenging to create a meaningful map given the size of the network.
The local authorities spatial object is necessary in order to use the od2line()
function from the stplanr
package. This is a very useful function transforms origin to destination (OD) tables to linear spatial objects. In order for this function to work we need the above spatial object with the zones of the origin and destination flows. Importantly it needs to only include the zone codes (i.e. the local authority codes), which should match with the origin and destination codes.This is the la
spatial object of the local authorities in England and Wales, which has already been loaded in R.
The below code just plots the boundaries of local authorities.
ggplot(la) +
geom_sf() +
ggtitle("Local authorities")
Now let’s do some clean-up of the commuting.all
data frame in order to convert it to a spatial object using the od2line()
function.
# We start by plotting a histogram of the data. We are using ggplot() as the output
# is nicer, but the simpler hist() could also be used
options(scipen=999) # It prevents R from using scientific notation for numbers
ggplot(commuting.all,
aes(x=weight)) +
geom_histogram() +
geom_vline(aes(xintercept=mean(weight)), # This line of code adds a vertical line to represent the mean
color="blue", linetype="dashed", size=1)
Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
ℹ Please use `linewidth` instead.
As you can see the flow data is very skewed. So, let’s truncate the data and plot a histogram for flows between origin and destinations will less than 1000 people.
ggplot(commuting.all[commuting.all$weight < 1000,],
aes(x=weight)) +
geom_histogram() +
geom_vline(aes(xintercept=mean(weight)),
color="blue",
linetype="dashed",
size=1)
There is a very large number of local authority pairs with very few people commuting between these OD pairs. So, in order to decrease the data and the mapping complexity we will keep only the OD pairs with more than 5 commuters.
<- commuting.all %>%
commuting.all.truncated filter(weight > 5) %>%
glimpse()
Rows: 41,659
Columns: 3
$ o <chr> "E41000001", "E41000001", "E41000001", "E41000001", "E41000001"…
$ d <chr> "E41000002", "E41000003", "E41000004", "E41000005", "E41000010"…
$ weight <dbl> 1591, 534, 3865, 433, 8, 24, 6, 30, 6, 6, 10, 8, 6, 7, 7, 7, 9,…
Question: How many lines did we filter out?
The next chunk of code converts the origin-destination table to a spatial object using the corresponding zones spatial object (la) that we have already loaded.
# od2line() has some strict requirement regarding data structure.
# Check ?od2line
# Therefore, we kept only the local authority code and name.
# The actual requirement is to have the the zone code as the
# first column of the zone object.
# If you remember, we run the following when we loaded the la object:
# la.names <- as.data.frame(la) %>%
# select(cmlad11cd, cmlad11nm) # all we need is the LA names and codes
<- od2line(flow = commuting.all.truncated,
travel_network zones = la)
# Just to see the class of the new spatial object
class(travel_network)
[1] "sf" "data.frame"
plot(travel_network)
This is a naive plot of the spatial network. We can guess the shape of England and Wales, but this is like a hairball network and far from being useful. In order to produce a more useful visualisation we will employ the leaflet
package, which produces interactive maps using JaveScript
Libraries.
# this is the colour pallet we are going to use based on 5 quantiles
<- colorQuantile("YlOrBr", domain = travel_network$weight, n=5)
Flow_pal
leaflet() %>%
addTiles() %>%
addPolylines(
data = travel_network,
weight = .1,
color = ~Flow_pal(weight),
opacity = .6) %>%
addLegend("topright",
pal = Flow_pal,
values = travel_network$weight,
title = "Commuting flows in 2011")