Bermuda Triangles: GNNs Fail to Detect Simple Topological Structures

Arseny Tolmachev, Akira Sakai, Masaru Todoriki, Koji Maruhashi

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2105.00134/code)

Keywords: graph neural networks, graph topology

TL;DR: Graph neural networks can't reliably detect triangle structures in a graph

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 available on https://github.com/FujitsuLaboratories/bermudatriangles.