Local iterative algorithms for approximate symmetry guided by network centralities

TL;DR

This paper introduces a heuristic local iterative algorithm that leverages network centralities to efficiently approximate symmetries in complex networks, improving upon existing methods sensitive to small changes.

Contribution

It proposes a novel heuristic extension of iterative search algorithms using network centralities to better approximate network symmetries under uncertainty.

Findings

Centralities guide the search towards better symmetry approximations.

The method outperforms previous algorithms in finding approximate automorphisms.

Network centralities effectively navigate the large permutation space.

Abstract

Recently, the influence of potentially present symmetries has begun to be studied in complex networks. A typical way of studying symmetries is via the automorphism group of the corresponding graph. Since complex networks are often subject to uncertainty and automorphisms are very sensitive to small changes, this characterization needs to be modified to an approximate version for successful application. This paper considers a recently introduced approximate symmetry of complex networks computed as an automorphism with acceptance of small edge preservation error, see Liu 2020. This problem is generally very hard with respect to the large space of candidate permutations, and hence the corresponding computation methods typically lead to the utilization of local algorithms such as the simulated annealing used in the original work. This paper proposes a new heuristic algorithm extending such iterative search algorithm method by using network centralities as heuristics. Centralities are shown to be a good tool to navigate the local search towards more appropriate permutations and lead to better search results.