Emergence of Symmetry in Complex Networks

TL;DR

This paper investigates the origins of symmetry in complex networks, revealing that similar linkage patterns among nodes with comparable degrees lead to symmetry, and introduces an improved model that reproduces this property.

Contribution

It identifies similar linkage pattern as the key mechanism behind network symmetry and proposes an enhanced BA model to simulate this phenomenon.

Findings

Symmetry arises from similar linkage patterns among nodes.

An improved BA model reproduces real network symmetry.

Network symmetry is linked to local symmetric motifs.

Abstract

Many real networks have been found to have a rich degree of symmetry, which is a very important structural property of complex network, yet has been rarely studied so far. And where does symmetry comes from has not been explained. To explore the mechanism underlying symmetry of the networks, we studied statistics of certain local symmetric motifs, such as symmetric bicliques and generalized symmetric bicliques, which contribute to local symmetry of networks. We found that symmetry of complex networks is a consequence of similar linkage pattern, which means that nodes with similar degree tend to share similar linkage targets. A improved version of BA model integrating similar linkage pattern successfully reproduces the symmetry of real networks, indicating that similar linkage pattern is the underlying ingredient that responsible for the emergence of the symmetry in complex networks.