Graph Convolutional Networks with Dual Message Passing for Subgraph Isomorphism Counting and Matching

TL;DR

This paper introduces Dual Message Passing Neural Networks (DMPNNs) that leverage edge-to-vertex dual graphs to improve subgraph isomorphism counting and matching, demonstrating robust performance on synthetic and real heterogeneous graphs.

Contribution

It proposes a novel dual message passing framework based on edge-to-vertex dual graphs, enhancing substructure learning for isomorphism tasks.

Findings

DMPNNs outperform existing methods in subgraph isomorphism tasks.

The approach effectively combines node and edge representations.

Experimental results validate robustness on diverse graph datasets.

Abstract

Graph neural networks (GNNs) and message passing neural networks (MPNNs) have been proven to be expressive for subgraph structures in many applications. Some applications in heterogeneous graphs require explicit edge modeling, such as subgraph isomorphism counting and matching. However, existing message passing mechanisms are not designed well in theory. In this paper, we start from a particular edge-to-vertex transform and exploit the isomorphism property in the edge-to-vertex dual graphs. We prove that searching isomorphisms on the original graph is equivalent to searching on its dual graph. Based on this observation, we propose dual message passing neural networks (DMPNNs) to enhance the substructure representation learning in an asynchronous way for subgraph isomorphism counting and matching as well as unsupervised node classification. Extensive experiments demonstrate the robust performance of DMPNNs by combining both node and edge representation learning in synthetic and real heterogeneous graphs. Code is available at https://github.com/HKUST-KnowComp/DualMessagePassing.