  Voxel hierarchy on dynamic brain graphs is produced by k core percolation on
functional dynamic amplitude correlation of resting-state fMRI. Directed graphs
and their afferent/efferent capacities are produced by Markov modeling of the
universal cover of undirected graphs simultaneously with the calculation of
volume entropy. Positive and unsigned negative brain graphs were analyzed
separately on sliding-window representation to underpin the visualization and
quantitation of mental dynamic states with their transitions. Voxel hierarchy
animation maps of positive graphs revealed abrupt changes in coreness k and
kmaxcore, which we called mental state transitions. Afferent voxel capacities
of the positive graphs also revealed transient modules composed of dominating
voxels/independent components and their exchanges representing mental state
transitions. Animation and quantification plots of voxel hierarchy and afferent
capacity corroborated each other in underpinning mental state transitions and
afferent module exchange on the positive directed functional connectivity
graphs. We propose the use of spatiotemporal trajectories of voxels on positive
dynamic graphs to construct hierarchical structures by k core percolation and
quantified in- and out-flows of information of voxels by volume
entropy/directed graphs to subserve diverse resting mental state transitions on
resting-state fMRI graphs in normal human individuals.
