Structural Equivalence in Subgraph Matching

TL;DR

This paper explores how symmetry and structural equivalence can be leveraged to improve the efficiency of subgraph matching algorithms, demonstrating methods that accelerate search and reduce solution space complexity.

Contribution

It introduces rigorous definitions of structural equivalence and adapts search routines to utilize symmetries, extending these methods to multiplex graphs and large real-world networks.

Findings

Symmetry-aware algorithms outperform standard methods in benchmark tests.

Structural equivalence reduces search space and accelerates subgraph matching.

Effective on large multiplex networks from various domains.

Abstract

Symmetry plays a major role in subgraph matching both in the description of the graphs in question and in how it confounds the search process. This work addresses how to quantify these effects and how to use symmetries to increase the efficiency of subgraph isomorphism algorithms. We introduce rigorous definitions of structural equivalence and establish conditions for when it can be safely used to generate more solutions. We illustrate how to adapt standard search routines to utilize these symmetries to accelerate search and compactly describe the solution space. We then adapt a state-of-the-art solver and perform a comprehensive series of tests to demonstrate these methods' efficacy on a standard benchmark set. We extend these methods to multiplex graphs and present results on large multiplex networks drawn from transportation systems, social media, adversarial attacks, and knowledge graphs.