A new network structure entropy based on maximum flow

Abstract

Entropy is an index to reflect the heterogeneity of network structure. By introducing the concept of network flow which comprehensively considers radial measurement and betweenness measurement, we define a new network structure entropy index to solve the problem that classical entropy indices cannot effectively reflect heterogeneity of the global network. Analysis results concerning specific network (e.g. public data set Dolphins network) indicate that this new entropy index can reflect the real topological structure of network, and effectively overcome the shortcomings of other network entropy indices to some extent. The theoretical analyses and simulation experiments on Erdös-Renyi random network, nearest-neighbor coupled network, star network, Barabási-Albert scale-free network, Benchmark network, and the Watts-Strogatz small-world network further prove the effectiveness and applicability of this new network structure entropy index to describe the characteristics of ordinary complex network structures.