The topology of higher-order complexes associated with brain-function hubs in human connectomes

TL;DR

This study explores the higher-order topological structure of human brain connectomes, focusing on key hubs and their complex interactions, revealing differences between female and male brains and emphasizing the importance of higher-order connectivity.

Contribution

It introduces a detailed analysis of simplicial complexes in brain networks, highlighting the role of topological dimensions and weight-dependent heterogeneity in understanding brain function.

Findings

Identified core networks around key brain hubs.

Demonstrated changes in network structure with weight thresholds.

Highlighted differences between female and male connectomes.

Abstract

Higher-order connectivity in complex systems described by simplexes of different orders provides a geometry for simplex-based dynamical variables and interactions. Simplicial complexes that constitute a functional geometry of the human connectome can be crucial for the brain complex dynamics. In this context, the best-connected brain areas, designated as hub nodes, play a central role in supporting integrated brain function. Here, we study the structure of simplicial complexes attached to eight global hubs in the female and male connectomes and identify the core networks among the affected brain regions. These eight hubs (Putamen, Caudate, Hippocampus and Thalamus-Proper in the left and right cerebral hemisphere) are the highest-ranking according to their topological dimension, defined as the number of simplexes of all orders in which the node participates. Furthermore, we analyse the weight-dependent heterogeneity of simplexes. We demonstrate changes in the structure of identified core networks and topological entropy when the threshold weight is gradually increased. These results highlight the role of higher-order interactions in human brain networks and provide additional evidence for (dis)similarity between the female and male connectomes.