Neural Subgraph Isomorphism Counting

TL;DR

This paper introduces a neural learning framework for counting subgraph isomorphisms, enabling scalable and faster approximate counting in large graphs, with applications demonstrated on chemical datasets.

Contribution

The paper proposes a novel neural network-based method that generalizes subgraph isomorphism counting, significantly improving speed over traditional algorithms while maintaining acceptable accuracy.

Findings

Speedup of 10-1000 times over VF2 algorithm

Effective transfer learning demonstrated on MUTAG dataset

Linear time approximation for large pattern and graph counts

Abstract

In this paper, we study a new graph learning problem: learning to count subgraph isomorphisms. Different from other traditional graph learning problems such as node classification and link prediction, subgraph isomorphism counting is NP-complete and requires more global inference to oversee the whole graph. To make it scalable for large-scale graphs and patterns, we propose a learning framework which augments different representation learning architectures and iteratively attends pattern and target data graphs to memorize subgraph isomorphisms for the global counting. We develop both small graphs (<= 1,024 subgraph isomorphisms in each) and large graphs (<= 4,096 subgraph isomorphisms in each) sets to evaluate different models. A mutagenic compound dataset, MUTAG, is also used to evaluate neural models and demonstrate the success of transfer learning. While the learning based approach is inexact, we are able to generalize to count large patterns and data graphs in linear time compared to the exponential time of the original NP-complete problem. Experimental results show that learning based subgraph isomorphism counting can speed up the traditional algorithm, VF2, 10-1,000 times with acceptable errors. Domain adaptation based on fine-tuning also shows the usefulness of our approach in real-world applications.