Symmetry based Structure Entropy of Complex Networks

TL;DR

This paper introduces a novel structure entropy based on automorphism partition to accurately measure the heterogeneity of complex networks, outperforming degree-based methods and revealing that real networks are more heterogeneous and less symmetric than previously thought.

Contribution

The paper proposes a new automorphism-based structure entropy that more precisely quantifies network heterogeneity compared to existing degree-based entropies.

Findings

Automorphism-based entropy better captures network heterogeneity.

Real networks are more heterogeneous than degree-based measures suggest.

Structural heterogeneity is negatively correlated with network symmetry.

Abstract

Precisely quantifying the heterogeneity or disorder of a network system is very important and desired in studies of behavior and function of the network system. Although many degree-based entropies have been proposed to measure the heterogeneity of real networks, heterogeneity implicated in the structure of networks can not be precisely quantified yet. Hence, we propose a new structure entropy based on automorphism partition to precisely quantify the structural heterogeneity of networks. Analysis of extreme cases shows that entropy based on automorphism partition can quantify the structural heterogeneity of networks more precisely than degree-based entropy. We also summarized symmetry and heterogeneity statistics of many real networks, finding that real networks are indeed more heterogenous in the view of automorphism partition than what have been depicted under the measurement of degree based entropies; and that structural heterogeneity is strongly negatively correlated to symmetry of real networks.