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About this paper
Marzieh Eidi, Nina Otter
Marzieh Eidi and Nina Otter present a geometric framework to define and compute structural and regular equivalences in graphs and hypergraphs. Their work establishes that Ollivier-Ricci curvature (ORC) equal to 1 precisely characterizes structural equivalence in graphs and weak structural equivalence in hypergraphs, while connected components of n-neighbourhood graphs are shown to induce regular classes.
Key insights
- Structural equivalence in graphs (and weak structural equivalence in hypergraphs) is precisely characterized by an Ollivier-Ricci Curvature of 1, establishing a direct link between geometry and combinatorial structure.
- Connected components of n-neighbourhood graphs directly correspond to regular classes, providing a potentially computationally efficient method for finding these partitions.
- Different hypergraph random walk models (Equal-Nodes vs. Equal-Edges) lead to a hierarchy of structural equivalence notions, revealing nuanced ways similarity can be defined in higher-order networks.
Summary by alphaXiv.
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