The discovery of population differences in network community structure: new methods and applications to brain functional networks in schizophrenia.

The modular organization of the brain network can vary in two fundamental ways. The amount of inter- versus intra-modular connections between network nodes can be altered, or the community structure itself can be perturbed, in terms of which nodes belong to which modules (or communities). Alterations have previously been reported in modularity, which is a function of the proportion of intra-modular edges over all modules in the network. For example, we have reported that modularity is decreased in functional brain networks in schizophrenia: There are proportionally more inter-modular edges and fewer intra-modular edges. However, despite numerous and increasing studies of brain modular organization, it is not known how to test for differences in the community structure, i.e., the assignment of regional nodes to specific modules. Here, we introduce a method based on the normalized mutual information between pairs of modular networks to show that the community structure of the brain network is significantly altered in schizophrenia, using resting-state fMRI in 19 participants with childhood-onset schizophrenia and 20 healthy participants. We also develop tools to show which specific nodes (or brain regions) have significantly different modular communities between groups, a subset that includes right insular and perisylvian cortical regions. The methods that we propose are broadly applicable to other experimental contexts, both in neuroimaging and other areas of network science.