Figure 4. . Identification of hubs, changes in graph-theoretic measures at the node level, and provincial/connecter hub classification. (A) Cortical areas of the macaque N = 47 connectome sorted by degree for the empirical and each perturbed network. Hubs are defined as nodes that have a total degree (in-degree plus out-degree) at least 1 standard deviation above the mean, and super hubs are defined as nodes that have a degree at least 1.5 standard deviations above the mean. The density-preserving results are from an illustrative single trial and show the standard deviation in degree for each node (over 1,000 trials). (B) Percentage of core, hub, and super-hub nodes across the perturbed networks of all six connectomes that retain correct classification according to their empirical connectome (as the mean over 1,000 trials). (C) Change in the participation index of each brain region from the empirical macaque N = 47 connectome to an illustrative case of the density-preserving network. (D) Identification and classification of hub nodes for the empirical (blue) macaque N = 47 connectome and an illustrative case of the density-preserving (red) network. The dotted line represents the hub definition based on the degree, and the dashed line represents the subclassification of hubs as either connector (Y > 0.35) or provincial (Y ≤ 0.35), based on the participation index. (E) Mean probability (across all connectomes over 1,000 trials) that hub nodes will cross over either, or both, of the threshold lines following density-preserving alterations in directionality, resulting in a classification that is inconsistent with the empirical connectomes. (A–E) Each perturbed network has 100% of unidirectional connections altered. Hub nodes are defined in the empirical network and retain the same definition in the perturbed networks.