Symmetry consideration in identifying network structures

TL;DR

This paper introduces a symmetry-based approach to community detection in networks, emphasizing the equivalence of a network and its complement, and presents a method capable of identifying hierarchical structures without resolution limits.

Contribution

It proposes a novel symmetric community detection scheme based on topological symmetry, addressing limitations of existing methods and revealing hierarchical community structures.

Findings

Method has no resolution limit

Can detect hierarchical community structures

Community structure unlikely due to random fluctuations

Abstract

The topological information of a network can be retrieved equivalently from its complement consisting of the same nodes but complementary edges. Hence the partition of a network into certain substructures based on given criteria should be the same as that of its complement based on the equivalent criteria if the topological information is considered exclusively. This symmetry of partitioning between a network and its complement is due to the equivalence of their topological information and hence should be respected regardless of the detailed characteristics of the substructures considered. In this work we suggest this symmetry consideration as a general guideline and propose a symmetric community detection scheme to show its implications. Our method has no resolution limit and can be used to detect hierarchical community structures at different levels. Our study also suggests that the community structure is unlikely a result of random fluctuations in large networks.