The topological hierarchy of a complex network was analyzed using each node's degree as a proxy for its importance. A simple dynamical process used to construct networks which are either maximally or minimally hierarchical was proposed. The hierarchical structure was quantified as the fraction of shortest paths that are also hierarchical. The results show that for random scale-free topologies the extent of topological hierarchy smoothly decline with γ, the exponent of a degree distribution, reaching its highest possible value for γ ≤ 2 and quickly approaching zero for γ > 3.
ASJC Scopus subject areas
- Physics and Astronomy(all)