# Structural Equivalence in Subgraph Matching

arXiv: https://arxiv.org/abs/2301.03161 · HTML: https://mlsanity.com/paper/2301.03161/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jan 2023.

## Built on by (most cited first, 2 of 2)

- [Gotta match 'em all: Solution diversification in graph matching matched filters](https://mlsanity.com/paper/2308.13451/) (2023)
- [From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontier](https://mlsanity.com/paper/2607.07779/) (2026)

## Abstract (arXiv)

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.