Modularity (networks)

Modularity, Community structure, Community detection

A fundamental quantity that measures how strong the given partitions are based on the difference between the actual number of within-partition edges and the expected number of within-partition edges based on the Configuration model.

Modularity maximization

A commonly used method for Community detection is simply to find a partition that maximizes the modularity.

One critical issue is that modularity maximization would find spurious communities even in random networks. It is possible to consider a null model (random graphs) and compare the modularity to test whether we can reject the hypothesis that the actual network cannot be distinguished from the random networks in terms of its maximized modularity. However, this does not still tell us which partition is significant. See Significant community structure via statistical tests? by Tiago Peixoto