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Advantages to modeling relational data using hypergraphs versus graphs

Driven by the importance of relational aspects of data to decision-making, graph algorithms have been developed, based on simplified pairwise relationships, to solve a variety of problems. However, evidence has shown that hypergraphs-generalizations of graphs with (hyper)edges that connect any number of vertices-can better model complex, non-pairwise relationships in data and lead to better informed decisions. In this work, we compare graph and hypergraph models in the context of spectral clustering. For these problems, we demonstrate that hypergraphs are computationally more efficient and can better model complex, non-pairwise relationships for many datasets.