  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.
