Title: Weisfeiler and Leman Follow the Arrow of Time: Expressive Power of Message Passing in Temporal Event Graphs
Primary area: learning on graphs and other geometries & topologies
Keywords: temporal graphs, temporal graph isomorphism, machine learning, graph neural networks

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 with synthetic and real-world temporal graphs shows that our approach performs well in a temporal graph classification experiment.

TL;DR: We introduce a new notion of temporal graph isomorphism that respects the arrow of time and generalize the Weisfeiler-Leman algorithm to account for this notion.