Bermuda Triangles: GNNs Fail to Detect Simple Topological Structures

TL;DR

This paper demonstrates that common GNN architectures struggle with simple topological tasks like triangle detection and clique distance, challenging assumptions about their ability to capture graph topology.

Contribution

It introduces synthetic topological tasks revealing GNN limitations, with publicly available datasets for further research.

Findings

GNNs perform poorly on triangle detection

GNNs fail to accurately measure clique distances

Results challenge assumptions about GNNs capturing topology

Abstract

Most graph neural network architectures work by message-passing node vector embeddings over the adjacency matrix, and it is assumed that they capture graph topology by doing that. We design two synthetic tasks, focusing purely on topological problems -- triangle detection and clique distance -- on which graph neural networks perform surprisingly badly, failing to detect those "bermuda" triangles. Datasets and their generation scripts are publicly available on github.com/FujitsuLaboratories/bermudatriangles and dataset.labs.fujitsu.com.