A Message-Passing Algorithm for Graph Isomorphism

TL;DR

This paper introduces a message-passing algorithm inspired by belief propagation to determine graph isomorphism by transforming graphs into canonical bipartite representations and comparing generated fingerprints.

Contribution

The paper presents a novel message-passing approach for graph isomorphism that uses canonical bipartite graph representations and fingerprint matching.

Findings

The algorithm accurately identifies isomorphic graphs.

It efficiently distinguishes non-isomorphic graphs.

The method is comparable or superior to existing algorithms.

Abstract

A message-passing procedure for solving the graph isomorphism problem is proposed. The procedure resembles the belief-propagation algorithm in the context of graphical models inference and LDPC decoding. To enable the algorithm, the input graphs are transformed into intermediate canonical representations of bipartite graphs. The matching procedure injects specially designed input patterns to the canonical graphs and runs a message-passing algorithm to generate two output fingerprints that are matched if and only if the input graphs are isomorphic.