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 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 for assortative hypergraphs. 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. We validate our results with both synthetic and empirical datasets.
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Research Article|
May 06 2022
Hypergraph assortativity: A dynamical systems perspective
Special Collection:
Dynamics on Networks with Higher-Order Interactions
Nicholas W. Landry
;
Nicholas W. Landry
a)
Department of Applied Mathematics, University of Colorado at Boulder
, Boulder, Colorado 80309, USA
a)Author to whom correspondence should be addressed: nicholas.landry@colorado.edu
Search for other works by this author on:
Juan G. Restrepo
Juan G. Restrepo
b)
Department of Applied Mathematics, University of Colorado at Boulder
, Boulder, Colorado 80309, USA
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a)Author to whom correspondence should be addressed: nicholas.landry@colorado.edu
b)
Electronic mail: juanga@colorado.edu
Note: This article is part of the Focus Issue, Dynamics on Networks with Higher-Order Interactions.
Chaos 32, 053113 (2022)
Article history
Received:
January 30 2022
Accepted:
April 12 2022
Citation
Nicholas W. Landry, Juan G. Restrepo; Hypergraph assortativity: A dynamical systems perspective. Chaos 1 May 2022; 32 (5): 053113. https://doi.org/10.1063/5.0086905
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