  Introduced recently, the concept of hierarchical degree allows a more
complete characterization of the topological context of a node in a complex
network than the traditional node degree. This article presents analytical
characterization and studies of the density of hierarchical degrees in random
and scale free networks. The obtained results allowed the identification of a
hierarchy-dependent power law for the degrees of nodes in random complex
networks, with Poisson density for the first hierarchical degree (obtained
through master equation approach). Exact results were obtained for the second
hierarchical degree in scale free networks.
