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A major objective of graph-based pattern recognition is to quantify the similarity between two graphs. One method, error-tolerant graph matching, assigns a cost for structural differences. More recent approaches involve graph kernels or graph neural networks. In this paper, we introduce a novel approach using graph neural networks to embed graph nodes into real vector spaces. We then compute topological invariants over nested simplicial complexes and derive a similarity value. Extensive experiments show that our method can achieve comparable classification performance of other algorithms while significantly reducing computation time.

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Learning Graph Similarity by Counting Holes in Simplicial Complexes

  • 会议论文

  • 发表日期：

    2025年

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  • Kalvin Dobler,
  • Kaspar Riesen

摘要

A major objective of graph-based pattern recognition is to quantify the similarity between two graphs. One method, error-tolerant graph matching, assigns a cost for structural differences. More recent approaches involve graph kernels or graph neural networks. In this paper, we introduce a novel approach using graph neural networks to embed graph nodes into real vector spaces. We then compute topological invariants over nested simplicial complexes and derive a similarity value. Extensive experiments show that our method can achieve comparable classification performance of other algorithms while significantly reducing computation time.