Weisfeiler and Leman Follow the Arrow of Time: Expressive Power of Message Passing in Temporal Event Graphs

TL;DR

This paper introduces a new theoretical framework and a message passing scheme for temporal graph neural networks that better capture causal topology influenced by the arrow of time.

Contribution

It develops a temporal generalization of the Weisfeiler-Leman algorithm and a message passing scheme based on event graph representations.

Findings

The approach effectively distinguishes non-isomorphic temporal graphs.

The message passing scheme performs well in classification tasks.

Theoretical analysis highlights advantages over existing methods.

Abstract

An important characteristic of temporal graphs is how the directed arrow of time influences their causal topology, i.e., which nodes can possibly influence each other causally via time-respecting paths. The resulting patterns are often neglected by temporal graph neural networks (TGNNs). To formally analyze the expressive power of TGNNs, we lack a generalization of graph isomorphism to temporal graphs that fully captures their causal topology. Addressing this gap, we introduce the notion of consistent event graph isomorphism, which utilizes a time-unfolded representation of time-respecting paths in temporal graphs. We compare this definition with existing notions of temporal graph isomorphisms. We illustrate and highlight the advantages of our approach and develop a temporal generalization of the Weisfeiler-Leman algorithm to heuristically distinguish non-isomorphic temporal graphs. Building on this theoretical foundation, we derive a novel message passing scheme for temporal graph neural networks that operates on the event graph representation of temporal graphs. An experimental evaluation shows that our approach performs well in a temporal graph classification experiment.