Hierarchy measures in complex networks.
Using each node's degree as a proxy for its importance, the topological hierarchy of a complex network is introduced and quantified. We propose a simple dynamical process used to construct networks which are either maximally or minimally hierarchical. Comparison with these extremal cases as well as with random scale-free networks allows us to better understand hierarchical versus modular features in several real-life complex networks. For random scale-free topologies the extent of topological hierarchy is shown to smoothly decline with gamma, the exponent of a degree distribution, reaching its highest possible value for gamma</=2 and quickly approaching zero for gamma>3.
Trusina
Ala
A
Department of Physics, Umeå University, 90187 Umeå, Sweden. trusina@tp.umu.se
Maslov
Sergei
S
Minnhagen
Petter
P
Sneppen
Kim
K