Hypergraph Similarity Measures

In this paper we present a novel framework for hypergraph similarity measures (HSMs) for hypergraph comparison. Hypergraphs are generalizations of graphs in which edges may connect any number of vertices, thereby representing multi-way relationships which are ubiquitous in many real-world networks including neuroscience, social networks, and bioinformatics. We propose two approaches for developing HSMs. The first approach is based on transforming the hypergraph into a graph representation, e.g., clique and star expansion, and then invoking the standard graph similarity measures. The second approach relies on a tensor-based representation of hypergraphs which intrinsically captures multi-way relations, and define similarity measures using tensor algebraic notions. Within each approach we present a collection of measures which either assess hypergraph similarity at a specific scale e.g., local, mesoscopic or global, or provide a more holistic multi-scale comparison. We discuss the advantages and disadvantages of the two proposed approaches, and demonstrate their performance on synthetic hypergraphs and hypergraphs derived from experimental biological datasets.