Modularity score comparion between different algorithms in network analysis

Question

[The Last Word]

I used different algorithms for splitting my large gene network into different sub-networks using Cytoscape. I compared the modularity scores and decided that the algorithm with the best modularity score will be used for clustering the network.

My colleague came up with the argument that modularity scores can only be compared for different number of clusters being created by the same algorithm.

So, my question is if modularity scores can be used to compare between different algorithms or only in the case of the same algorithm producing different number of clusters.

Answer 1

[Jean-Karim Heriche]

The modularity score of a graph is the sum over all clusters of the number of edges in a cluster minus the number of edges expected by chance in the cluster. However, there are a few different ways of computing it (essentially due to how one defines edges expected by chance) but once a given definition of modularity is chosen, the modularity score of a graph only depends on the choice of clusters in the graph. What this means is: choose a definition of modularity then compute it for every partition of the graph you're interested in (possibly using different clustering algorithms). However, there are already algorithms that find the clusters that maximize the modularity so in principle, clustering algorithms that optimize another objective function are not expected to give the best modularity (unless of course they end up with the same partitioning of the graph).