## Finding communities in networks with R and igraph

Finding communities in networks is often a common task under the paradigm of complex systems. Doing it in **R** is very easy and there are several ways to do community partitioning of graphs using very different packages. The one I’m talking here is **ipgrah**.

**igraph** is a lovely library to work with graphs. 95% of what you’ll need is available in **igraph** with the advantage that the libraries are written in C and therefore are fast as hell.

Ok, now for the list of algorithms that you might be interested:

**walktrap.community**

This algorithm finds densely connected subgraphs by performing random walks. The idea is that random walks will tend to stay inside communities instead of jumping to other communities.

Pascal Pons, Matthieu Latapy: Computing communities in large networks using random walks, http://arxiv.org/abs/physics/0512106

**edge.betweenness.community**

This algorithm is the Girvan-Newman algorithm. Basically it is a divisive algorithm where at each step the edge with the highest betweenness is removed from the graph. For each division you can compute the modularity of the graph and then choose to cut the dendrogram where the process gives you the highest value of modularity.

M Newman and M Girvan: Finding and evaluating community structure in networks, Physical Review E 69, 026113 (2004)

**fastgreedy.community**

This algorithm is the Clauset-Newman-Moore algorithm. In this case the algorithm is agglomerative and at each step the merge is decided by the optimization of modularity that it produces as the result of the merge. This is very fast, but has the disadvantage of being a greedy algorithm, so it is might not produce the best overall community partitioning, although I find it very useful and very accurate.

A Clauset, MEJ Newman, C Moore: Finding community structure in very large networks, http://www.arxiv.org/abs/cond-mat/0408187

**spinglass.community**

This algorithm uses as spin-glass model and simulated annealing to find the communities inside a network.

J. Reichardt and S. Bornholdt: Statistical Mechanics of Community Detection, Phys. Rev. E, 74, 016110 (2006), http://arxiv.org/abs/cond-mat/0603718

M. E. J. Newman and M. Girvan: Finding and evaluating community structure in networks, Phys. Rev. E 69, 026113 (2004)

**An example:**

# First we load the ipgrah package library(igraph) # let's generate two networks and merge them into one graph. g2 <- barabasi.game(50, p=2, directed=F) g1 <- watts.strogatz.game(1, size=100, nei=5, p=0.05) g <- graph.union(g1,g2) # let's remove multi-edges and loops g <- simplify(g) # let's see if we have communities here using the # Grivan-Newman algorithm # 1st we calculate the edge betweenness, merges, etc... ebc <- edge.betweenness.community(g, directed=F) # Now we have the merges/splits and we need to calculate the modularity # for each merge for this we'll use a function that for each edge # removed will create a second graph, check for its membership and use # that membership to calculate the modularity mods <- sapply(0:ecount(g), function(i){ g2 <- delete.edges(g, ebc$removed.edges[seq(length=i)]) cl <- clusters(g2)$membership # March 13, 2014 - compute modularity on the original graph g # (Thank you to Augustin Luna for detecting this typo) and not on the induced one g2. modularity(g,cl) }) # we can now plot all modularities plot(mods, pch=20) # Now, let's color the nodes according to their membership g2<-delete.edges(g, ebc$removed.edges[seq(length=which.max(mods)-1)]) V(g)$color=clusters(g2)$membership # Let's choose a layout for the graph g$layout <- layout.fruchterman.reingold # plot it plot(g, vertex.label=NA) # if we wanted to use the fastgreedy.community agorithm we would do fc <- fastgreedy.community(g) com<-community.to.membership(g, fc$merges, steps= which.max(fc$modularity)-1) V(g)$color <- com$membership+1 g$layout <- layout.fruchterman.reingold plot(g, vertex.label=NA) |

try it!