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

Self-Organised Critical Dynamics as a Key to Fundamental Features of Complexity in Physical, Biological, and Social Networks

“…Another research line connects the hierarchical architecture of brain networks and SOC dynamics [61], also pointing out to the structural adaptation [62]. Recently, the occurrence of higher-order structures (simplicial complexes) in human connectomes were demonstrated [54,63]. The role of such complex topologies in brain dynamics was pointed out [64].…”

“…Data Availability Statement: This is a theoretical study. Figure 3a,c is based on publicly available data first collected and used in references [54,56], respectively, cf. Figure caption.…”

Homological scaffold via minimal homology bases

“…The possible applications in which the minimal scaffold could provide novel insight into the structure of brain data are many: any relatively small correlation matrix could be either compressed or its patterns analyzed, as is often the case in EEG 42,44,79,80 or neuronal 38 studies, and in fMRI ones when using rather coarse atlases (e.g. 81,82 ).…”

Topological Analysis of Interaction Patterns in Cancer-Specific Gene Regulatory Network: Persistent Homology Approach

“…These constructions can be described by simplices of different dimensions and hence, can be studied in the framework of Balance Theory and Topological Data Analysis (TDA). From TDA, we employ the Persistent Homology (PH) analysis tool, which is based on algebraic topology and has been applied to problems in a variety of fields such as network science, physics, chemistry, biology, and medicine [18][19][20][21][22][23][24][25][26][27][27][28][29][30][31][32] . PH has been previously used to study protein-protein interaction networks to inform cancer therapy by determining the correlation between Betti numbers and the survival of cancer patients 33 .…”