```
library(tidyverse)
library(igraph)
library(sand)
library(igraphdata)
```

# Network models in practice

## Setup

Pay attention on the packages `sand`

and `igraphdata`

. The first one contains all the different network datasets used by (Kolaczyk and Csárdi 2020). Then, the second one contain network data to be used together with the `igraph`

package. More information can be found here and here. Feel free to explore these network data on your own time.

## Aims of the practical

Simulate network models

Analyse their key attributes

Compare them

`igraph`

enables us to generate networks based on some of the some key network models we discussed. I list below some of these functions:

`sample_gnp()`

`sample_smallworld()`

`sample_pa()`

Go to `igraph`

’s webpage and familiarise yourselves with the syntax of these functions.

**Task**: Create three networks using these three functions with, let’s say, (n = 500) nodes each.

Visualise and compare these networks.

Importantly, just before you generate a network with one of the above three functions you will need to define a random seed for reproducibility reasons, e.g. `set.seed(55)`

.

**Question**: *Without* defining a random seed, generate a network as per the above, run some type of quick analysis about this network and then repeat the code by generating a second network with the exact same characteristics. Run the same analysis for the second network. Are the results the same?

Why do we need to define the random seed ?

## Examples of modelled networks

```
sample_gnp(n = 500, p = 0.02) %>%
plot(layout=layout_in_circle, vertex.label=NA)
```

```
sample_pa(n = 500, directed=FALSE) %>%
plot(layout=layout_in_circle, vertex.label=NA)
```

```
sample_smallworld(dim = 1, size = 500, nei = 5, p = 0.05) %>%
plot(layout=layout_in_circle, vertex.label=NA)
```

```
make_lattice(dim =1, length = 100, nei = 5) %>%
plot(vertex.label=NA)
```

**Challenge 1**: Think about the commuting datasets you used in the past tutorials. Is the commuters network Small World? Is it Scale-Free network?

**Challenge 2**: Can you demonstrate where would this graph sit on the scale between ranom and regular network using your knowledge centrality measures in I graph?

**Challenge 3**: Taking the commuters network or network of your choice, can you demonstrate the Bettencourt-West/Marshall’s law?

**Challange 4** Taking the data and model from the challange 3, can you find the value of (/beta) (the exponent)? What does that value mean for your variables and the phenomena tehy represent?

Extra resources: - Network Analysis in R from Dai Shizuka - Statistical Analysis of Network Data with R - Awesom Network Analysis: list of useful R packages (and much more) - R Graph Gallery _ Static and dynamic network visualization with R from Katya Ognyanova

## References

*Statistical Analysis of Network Data with r*. Second. Vol. 65. Springer.