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Hyperbolic disc embedding and  k -core percolation reveal the hierarchical structure of functional connectivity on resting-state fMRI (rsfMRI). Using 180 normal adults’ rsfMRI data from the human connectome project database, we visualized inter-voxel relations by embedding voxels on the hyperbolic space using the    $${\mathbb{S}}^{1} /{\mathbb{H}}^{2}$$  S 1 / H 2 model. We also conducted  k -core percolation on 30 participants to investigate core voxels for each individual. It recursively peels the layer off, and this procedure leaves voxels embedded in the center of the hyperbolic disc. We used independent components to classify core voxels, and it revealed stereotypes of individuals such as visual network dominant, default mode network dominant, and distributed patterns. Characteristic core structures of resting-state brain connectivity of normal subjects disclosed the distributed or asymmetric contribution of voxels to the  k  max -core, which suggests the hierarchical dominance of certain IC subnetworks characteristic of subgroups of individuals at rest.

Characteristic functional cores revealed by hyperbolic disc embedding and k-core percolation on resting-state fMRI