Question

The equation for Network Modularity is given on its wikipedia page (and in reputable books). I want to see it working in some code. I have found this is possible using the modularity library for igraph used with R (The R Foundation for Statistical Computing).

I want to see the example below (or a similar one) used in the code to calculate the modularity. The library gives on example but it isn’t really what I want.

Let us have a set of vertices V = {1, 2, 3, 4, 5} and edges E = {(1,5), (2,3), (2,4), (2,5) (3,5)} that form an undirected graph.

Divide these vertices into two communities: c1 = {2,3} and c2 = {1,4,5}. It is the modularity of these two communities that is to be computed.

Answer 1

library(igraph)
g <- graph(c(1,5,2,3,2,4,2,5,3,5))
membership <- c(1,2,2,1,1)
modularity(g, membership)

Some explanation here:

1. The vector I use when creating the graph is the edge list of the graph. (In igraph versions older than 0.6, we had to subtract 1 from the numbers because igraph uses zero-based vertex indices at that time, but not any more).

2. The i-th element of the membership vector membership gives the index of the community to which vertex i belongs.