Learning on Large Graphs using Intersecting Communities

TL;DR

This paper introduces a novel method for scalable graph learning by approximating large graphs with intersecting community graphs, enabling efficient message passing with linear memory and time complexity.

Contribution

The paper proposes a new approximation technique using intersecting community graphs and a constructive Weak Graph Regularity Lemma for efficient large graph learning.

Findings

Efficient graph learning on large non-sparse graphs demonstrated.

Linear memory and time complexity achieved for graph processing.

Empirical validation on node classification and spatio-temporal data.

Abstract

Message Passing Neural Networks (MPNNs) are a staple of graph machine learning. MPNNs iteratively update each node's representation in an input graph by aggregating messages from the node's neighbors, which necessitates a memory complexity of the order of the number of graph edges. This complexity might quickly become prohibitive for large graphs provided they are not very sparse. In this paper, we propose a novel approach to alleviate this problem by approximating the input graph as an intersecting community graph (ICG) -- a combination of intersecting cliques. The key insight is that the number of communities required to approximate a graph does not depend on the graph size. We develop a new constructive version of the Weak Graph Regularity Lemma to efficiently construct an approximating ICG for any input graph. We then devise an efficient graph learning algorithm operating directly on ICG in linear memory and time with respect to the number of nodes (rather than edges). This offers a new and fundamentally different pipeline for learning on very large non-sparse graphs, whose applicability is demonstrated empirically on node classification tasks and spatio-temporal data processing.