Modularity-based methods for structure and community discovery remain popular in the network neuroscience literature and enjoy a history of yielding meaningful neurobiological findings. All the while, the full potential of these methods remains limited in part by an absence of uncertainty quantification guarantees for use in downstream statistical inference. Here, we pursue this direction by revisiting the classical notion of modularity maximization in the analysis of adjacency and correlation matrices. We begin by considering certain latent space network models wherein high-dimensional matrix spectral properties can be precisely analyzed. We further propose and argue for the potential usefulness of several new, non-classical modularity-type network statistics. Our findings are applied to an analysis of dMRI and fMRI data in the study of schizophrenia.
Based on joint work with Konasale Prasad and Anirban Mitra.