Modular Brain Networks

Abstract

The development of new technologies for mapping structural and functional brain connectivity has led to the creation of comprehensive network maps of neuronal circuits and systems. The architecture of these brain networks can be examined and analyzed with a large variety of graph theory tools. Methods for detecting modules, or network communities, are of particular interest because they uncover major building blocks or subnetworks that are particularly densely connected, often corresponding to specialized functional components. A large number of methods for community detection have become available and are now widely applied in network neuroscience. This article first surveys a number of these methods, with an emphasis on their advantages and shortcomings; then it summarizes major findings on the existence of modules in both structural and functional brain networks and briefly considers their potential functional roles in brain evolution, wiring minimization, and the emergence of functional specialization and complex dynamics.

Keywords: clustering; connectome; functional connectivity; graph theory; hubs; resting state.

Figure 1

Schematic diagram of a brain network introducing basic terminology. (a) Networks consist of nodes and edges. The node degree corresponds to the number of edges that are attached to each node. (b) Networks can be decomposed into communities or modules. Connections (edges) are either linking nodes within modules or between modules. Highly connected nodes are hubs, and they either connect primarily with other nodes in the same community (provincial hub) or with nodes that belong to different communities (connector hub).

Figure 2

Illustration of multiscale modularity maximization for a structural (diffusion spectrum imaging) brain network (a). The size and brightness of connections indicate the number of subjects for which a connection is present and the log-transformed weight of that connection, respectively. For this network and for 20 random networks (rewired to preserve degree sequence), we maximized modularity using the Louvain algorithm (Blondel et al. 2008) and varied the resolution parameter from γ ∈ [0.5, 2.0] in increments of 0.05. As a function of γ, we obtained the mean modularity for the empirical and randomized networks, Q_empirical and Q_random. To report community structure, we chose the scale of γ at which the quality of empirical partitions exceeded that of random partitions by the greatest amount (b). At this scale (γ = 0.7) we further examined 100 partitions of the empirical network (c), which revealed that nodes’ community assignments were inconsistent. To resolve this variability, we performed consensus clustering, following Bassett et al. (2013) and Lancichinetti & Fortunato (2012). We constructed the association matrix (d) counting the number of times that node pairs were assigned to the same community. We generated many realizations of null partition ensembles by randomly permuting the columns of the partition ensemble matrix (e) and constructed null association matrices (f). We thresholded the empirical association matrix (g), retaining only elements greater than the maximum value of any null association matrix. We then reclustered the thresholded matrix to obtain consensus communities (h). Finally, we visualized community structure by reordering the connectivity matrix so that nodes in the same community would be next to one another (i).