arXiv AI November 5, 2026 By Jorge Luiz Franco, Arthur Queiroz Moura, Moacir Ponti, Amauri Souza

Message-passing graph persistence

The paper introduces Message‑Passing Graph Persistence (MGP), a new family of topological descriptors that integrates message‑passing into graph filtrations. By updating node embeddings at each filtration step and using them to determine persistence events and component representatives, MGP remains invariant under graph isomorphism and is proven to be strictly more expressive than existing PH‑based descriptors. Experiments on expressivity benchmarks and various graph classification and regression datasets demonstrate that MGP outperforms other PH‑based methods on most tasks.

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