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rigraph

Correct way of calculating modularity for weighted graphs

I have about 13000 genes which I am trying to cluster using igraph as follows:

g.communities <- edge.betweenness.community(as.undirected(g), weights = E(g)$weight)

which returns 97 communities with modularity 0.9773353:

 modularity(as.undirected(g), membership = g.communities$membership, weights = E(g)$weight)
 
 #0.9773353

when I tried to custom made the number of communities as below I get modularity of 0.0094:

 modularity(as.undirected(g), membership = cutat(g.communities, steps = 97), weights = 
 E(g)$weight)
 
 #0.0094

Shouldn't these functions return similar results? Also, is it possible to use the above function to find the correct number of clusters? (since by just increasing the steps the modularity always increases)

Finally g.communities$modularity returns a number for each vertex. Can these numbers be interpreted as the correlation of each vertex to its corresponding module?

Solution

  • You are using the steps argument of cut_at. This does not specify the number of communities, but the number of merging steps to perform on the dendrogram. If you want 97 communities, use cut_at(g.communities, no=97) or simply cut_at(g.communities, 97).

    That said, I do not suggest using edge.betweenness.community on weighted graphs at this time, for the reasons I described here.