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

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.

Machine Learning (cs.LG)

arXiv:2505.24438 [cs.LG]

(or arXiv:2505.24438v4 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2505.24438 Focus to learn more arXiv-issued DOI via DataCite

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