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 kmax-core, which suggests the hierarchical dominance of certain IC subnetworks characteristic of subgroups of individuals at rest.

Brain regions send and receive information through neuronal connections in an efficient way. In this paper, we modelled the information propagation in brain networks by a generalized Markov system associated with a new edge-transition matrix, based on the assumption that information flows through brain networks forever. From this model, we derived new global and local network measures, called a volume entropy and the capacity of nodes and edges on FDG PET and resting-state functional MRI. Volume entropy of a metric graph, a global measure of information, measures the exponential growth rate of the number of network paths. Capacity of nodes and edges, a local measure of information, represents the stationary distribution of information propagation in brain networks. On the resting-state functional MRI of healthy normal subjects, these measures revealed that volume entropy was significantly negatively correlated to the aging and capacities of specific brain nodes and edges underpinned which brain nodes or edges contributed these aging-related changes.

Objective Underconnectivity in the resting brain is not consistent in autism spectrum disorder (ASD). However, it is known that the functional connectivity of the default mode network is mainly decreased in childhood ASD. This study investigated the brain network topology as the changes in the connection strength and network efficiency in childhood ASD, including the early developmental stages.Methods In this study, 31 ASD children aged 2–11 years were compared with 31 age and sex-matched children showing typical development. We explored the functional connectivity based on graph filtration by assessing the single linkage distance and global and nodal efficiencies using resting-state functional magnetic resonance imaging. The relationship between functional connectivity and clinical scores was also analyzed.Results Underconnectivities within the posterior default mode network subregions and between the inferior parietal lobule and inferior frontal/superior temporal regions were observed in the ASD group. These areas significantly correlated with the clinical phenotypes. The global, local, and nodal network efficiencies were lower in children with ASD than in those with typical development. In the preschool-age children (2–6 years) with ASD, the anterior-posterior connectivity of the default mode network and cerebellar connectivity were reduced.Conclusion The observed topological reorganization, underconnectivity, and disrupted efficiency in the default mode network subregions and social function-related regions could be significant biomarkers of childhood ASD.

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Hyperbolic disc embedding and k-core percolation reveal the core structure of the functional connectivity on resting-state fMRI (rsfMRI). Inter-voxel relations were visualized on embedded hyperbolic discs, and their core composition was traced using k-core percolation. Using rsfMRI data of 180 normal adults from the Human Connectome Project database, scale-free intervoxel connectivity represented by IC-voxels composition, while visualized on hyperbolic discs using 𝕊1/ℍ2 model, showed the expected change of the largest component decreasing its size on k-core percolation eventually yielding the core structures of individuals. This kmax-core voxels-ICs composition revealed such stereotypes of individuals 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 kmax-core, which suggests the hierarchical dominance of certain IC subnetworks characteristic to subgroups of individuals at rest.