Node and edge nonlinear eigenvector centrality for hypergraphs

Abstract Network scientists have shown that there is great value in studying pairwise interactions between components a system. From linear algebra point of view, this involves defining and evaluating functions the associated adjacency matrix. Recent work indicates are further benefits from accounting directly for higher order interactions, notably through hypergraph representation where an edge may involve multiple nodes. Building on these ideas, we motivate, define analyze class spectral centrality measures identifying important nodes hyperedges hypergraphs, generalizing existing network science concepts. By exploiting latest developments nonlinear Perron−Frobenius theory, show how resulting constrained eigenvalue problems unique solutions can be computed efficiently via power method iteration. We illustrate realistic data sets.