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The human structural connectome has a complex internal communityorganization, characterized by a high degree of overlap and related tofunctional and cognitive phenomena. We explored connectivity properties inconnectome networks and showed that $k$-clique percolation of an anomalouslyhigh order is characteristic of the human structural connectome. The resultingstructural organization maintains a high local density of connectivitydistributed throughout the connectome while preserving the overall sparsity ofthe network. To analyze these findings, we proposed a novel model for theemergence of high-order clique percolation during network formation with aphase transition dynamic under constraints on connection length. Investigatingthe structural basis of functional brain subnetworks, we identified a directrelationship between their interaction and the formation of clique clusterswithin their structural connections. Based on these findings, we hypothesizethat the percolating clique cluster serves as a distributed boundary betweeninteracting functional subnetworks, showing the complex, complementary natureof their structural connections. We also examined the difference betweenindividual-specific and common structural connections and found that the latterplays a sustaining role in the connectivity of structural communities. At thesame time, the superiority of individual connections, in contrast to commonones, creates variability in the interaction of functional brain subnetworks.

Interaction of functional brain networks is formed by k-clique percolation in the human structural connectome