The Dynamics of Hierarchical Evolution of Complex Networks

TL;DR

This paper analyzes the hierarchical degree distribution in complex networks, revealing a hierarchy-dependent power law in random networks and exact results for scale-free networks, enhancing understanding of network topology.

Contribution

It provides analytical characterizations of hierarchical degrees, introducing hierarchy-dependent power laws and exact solutions for the second hierarchical degree in scale-free networks.

Findings

Hierarchy-dependent power law in random networks

Poisson density for first hierarchical degree

Exact results for second hierarchical degree in scale-free networks

Abstract

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.