Neural Subgraph Isomorphism Counting

Xin Liu, Haojie Pan, Mutian He, Yangqiu Song, Xin Jiang

TL;DR: In this paper, we study a new graph learning problem: learning to count subgraph isomorphisms.

Abstract: In this paper, we study a new graph learning problem: learning to count subgraph isomorphisms. Although the learning based approach is inexact, we are able to generalize to count large patterns and data graphs in polynomial time compared to the exponential time of the original NP-complete problem. Different from other traditional graph learning problems such as node classification and link prediction, subgraph isomorphism counting requires more global inference to oversee the whole graph. To tackle this problem, we propose a dynamic intermedium attention memory network (DIAMNet) which augments different representation learning architectures and iteratively attends pattern and target data graphs to memorize different 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. Experimental results show that learning based subgraph isomorphism counting can help reduce the time complexity with acceptable accuracy. Our DIAMNet can further improve existing representation learning models for this more global problem.

Keywords: subgraph isomorphism, graph neural networks

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:1912.11589/code)