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- W3198776220 abstract "The largest eigenvalue of the matrix describing a network's contact structure is often important in predicting the behavior of dynamical processes. We extend this notion to hypergraphs and motivate the importance of an analogous eigenvalue, the expansion eigenvalue, for hypergraph dynamical processes. Using a mean-field approach, we derive an approximation to the expansion eigenvalue and its associated eigenvector in terms of the degree sequence for uncorrelated hypergraphs. We introduce a generative model for hypergraphs that includes degree assortativity, and use a perturbation approach to derive an approximation to the expansion eigenvalue and its corresponding eigenvector for assortative hypergraphs. We validate our results with both synthetic and empirical datasets. We define the dynamical assortativity, a dynamically sensible definition of assortativity for uniform hypergraphs, and describe how reducing the dynamical assortativity of hypergraphs through preferential rewiring can extinguish epidemics." @default.
- W3198776220 created "2021-09-13" @default.
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- W3198776220 date "2021-09-02" @default.
- W3198776220 modified "2023-09-26" @default.
- W3198776220 title "Hypergraph dynamics: assortativity and the expansion eigenvalue" @default.
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