On Automorphism Groups of Networks

TL;DR

This paper investigates the size and structure of automorphism groups in real-world networks, revealing that many are highly symmetric, unlike classical random graph models, and explores how network topology influences these symmetries.

Contribution

It provides a detailed analysis of automorphism groups in empirical networks and links their structure to network topology, highlighting the prevalence of symmetry in real-world networks.

Findings

Many real-world networks are richly symmetric.

Automorphism group structure correlates with network topology.

Symmetry origins are discussed in the context of network formation.

Abstract

We consider the size and structure of the automorphism groups of a variety of empirical `real-world' networks and find that, in contrast to classical random graph models, many real-world networks are richly symmetric. We relate automorphism group structure to network topology and discuss generic forms of symmetry and their origin in real-world networks.