A Topological Perspective of Neural Network Structure

The wiring patterns of white matter tracts between brain regions inform functional capabilities of the neural network. Indeed, densely connected and cyclically arranged cognitive systems may communicate and thus perform distinctly. However, previously employed graph theoretical statistics are local in nature and thus insensitive to such global structure. Here we present an investigation of the structural neural network in eight healthy individuals using persistent homology. An extension of homology to weighted networks, persistent homology records both circuits and cliques (all-to-all connected subgraphs) through a repetitive thresholding process, thus perceiving structural motifs. We report structural features found across patients and discuss brain regions responsible for these patterns, finally considering the implications of such motifs in relation to cognitive function.