Nonlinear spectral centrality and core-periphery detection in hypergraphs

Network scientists have shown that there is great value in studying pairwise interactions between components in a system. Recently, however, there has been increased interest in the idea of accounting directly for higher-order interactions, notably through a simplicial complex or a hypergraph representation, where each edge (or simplex) may involve multiple nodes.

In this talk we present a nonlinear eigenvalue framework for incorporating higher-order interactions into network centrality measures. The proposed framework covers classical network coefficients such as matrix and tensor eigenvector centralities, but further allows for many interesting extensions. In particular, we show how this can be used to detect core and periphery structures in hypergraphs.

The underlying object of study is a constrained nonlinear eigenvalue or singular value problem. By exploiting recent developments in nonlinear Perron-Frobenius theory, we can provide guarantees of existence and uniqueness for the network measures, which we can also efficiently compute via a nonlinear power method. We illustrate the results on several example datasets.