Emergent high-order modularity in the human connectome network

Abstract

The usage of graphs to model relationships between variables is a common and well- established practice, but, like every model, it has its limitations. In this work, we explore a workaround for one of those limitations: the correct representation of interactions between more than 2 variables. Specifically, we investigate the 3-by-3 interaction between areas of the brain, modeled using 3-uniform hypergraphs. Given that the pairwise network models of the brain exhibit a modular property, i.e., the presence of vertex modules in the graph, our goal here is to determine if the modular property persists in hypergraphs, using modularity as our metric with a threshold set at 0.3. We utilized data from rs-fMRI scans of 1018 young adults, provided by the Human Connectome Project (HCP). For each patient, we obtained 2 rs-fMRI scans. We observed the 3-by-3 interactions between areas of the brain using two information theory metrics: Interaction Information (II) and Total Correlation (TC) to quantify the relation between the triplets. In total, we generated 12216 networks, 12 for each patient. We identified a modular structure that exhibited modularity above the threshold in 12202 hypergraphs, indicating the existence of a high-order modular property in the human brain. To further analyze the findings, we conducted a comparison using linear regression between the modularity and the clinical data of each patient, categorizing individuals by sex. We observed that the modularity has statistical significance (with a p-value below 0.05) in distinct datasets for males and females, with only one intersection between them. Additionally, we compared the clinical data where the high-order modularity has a p-value below 0.05 with the clinical data where the modularity of the pairwise method has a p-value below 0.05. We found that the intersection between the two methods is minimal, indicating that high-order approaches provide different information than pairwise methods.