Brain Network Modularity and Resilience Signaled by Betweenness Centrality Percolation Spiking

Modularity and resilience are fundamental properties of brain network organization and function. The interplay of these network characteristics is integral to understanding brain vulnerability, network efficiency, and neurocognitive disorders. One potential methodology to explore brain network modularity and resilience is through percolation theory, a sub-branch of graph theory that simulates lesions across brain networks. In this work, percolation theory is applied to connectivity matrices derived from functional MRI from human, mice, and null networks. Nodes, or regions, with the highest betweenness centrality, a graph theory quantifier that examines shortest paths, were sequentially removed from the network. This attack methodology led to a rapid fracturing of the network, resulting in two terminal modules connected by one transfer module. Additionally, preceding the rapid network fracturing, the average betweenness centrality of the network peaked in value, indicating a critical point in brain network functionality. Thus, this work introduces a methodological perspective to identify hubs within the brain based on critical points that can be used as an architectural framework for a neural network. By applying percolation theory to functional brain networks through a network phase-transition lens, network sub-modules are identified using local spikes in betweenness centrality as an indicator of brain criticality. This modularity phase transition provides supporting evidence of the brain functioning at a near-critical point while showcasing a formalism to understand the computational efficiency of the brain as a neural network.