Local Fragments, Global Gains: Subgraph Counting using Graph Neural Networks

Shubhajit Roy, Shrutimoy Das, Binita Maity, Anant Kumar, Anirban Dasgupta

Keywords: Subgraph Counting, Graph Neural Networks

TL;DR: We propose a fragmentation approach for exactly counting patterns using graph neural networks.

Abstract: Subgraph counting is a fundamental task for analyzing structural patterns in graph-structured data, particularly crucial for applications in computational biology and social network analysis, where identifying recurring motifs reveals functional properties and organizational structures. We propose a novel three-stage differentiable learning algorithm that computes the counts of various patterns by learning to combine the counts of its subpatterns. Our approach leverages localized versions of Weisfeiler-Leman (WL) algorithms and introduces a novel fragmentation technique that decomposes complex subgraphs into simpler patterns. This technique enables exact counting of all induced subgraphs of size at most $4$ using just $1$-WL. This method significantly improves upon existing Graph Neural Network(GNN) based approaches for subgraph counting, being computationally efficient, making it well-suited for learning combinatorial algorithms.

Submission Number: 10