Hyper-cores promote localization and efficient seeding in higher-order processes

Abstract

Going beyond networks, to include higher-order interactions of arbitrary sizes, is a major step to better describe complex systems. In the resulting hypergraph representation, tools to identify structures and central nodes are scarce. We consider the decomposition of a hypergraph in hyper-cores, subsets of nodes connected by at least a certain number of hyperedges of at least a certain size. We show that this provides a fingerprint for data described by hypergraphs and suggests a novel notion of centrality, the hyper-coreness. We assess the role of hyper-cores and nodes with large hyper-coreness in higher-order dynamical processes: such nodes have large spreading power and spreading processes are localized in central hyper-cores. Additionally, in the emergence of social conventions very few committed individuals with high hyper-coreness can rapidly overturn a majority convention. Our work opens multiple research avenues, from comparing empirical data to model validation and study of temporally varying hypergraphs.

Main document: 13 pages, 6 figures; Supplementary Material: 47 pages, 40 figures

References in corpus (11)

• The physics of higher-order interactions in complex systems
• What's in a crowd? Analysis of face-to-face behavioral networks
• Dynamics on higher-order networks: A review
• Does a Single Zealot Affect an Infinite Group of Voters ?
• Principles of scientific research team formation and evolution
• Non-equilibrium dynamics of language games on complex networks
• Evolution of Cooperation in the Presence of Higher-Order Interactions: from Networks to Hypergraphs
• A gentle introduction to the minimal Naming Game
• $(k,q)$-core decomposition of hypergraphs
• Interplay between $k$-core and community structure in complex networks
• Higher-order rich-club phenomenon in collaborative research grants

Cited by in corpus (12)

• The temporal dynamics of group interactions in higher-order social networks
• The theory of percolation on hypergraphs
• The nature of hypergraph $k$-core percolation problems
• Global topological synchronization of weighted simplicial complexes
• The structural evolution of temporal hypergraphs through the lens of hyper-cores
• Emerging Activity Temporal Hypergraph: a model for generating realistic time-varying hypergraphs
• Group adaptation drives opinion dynamics in higher-order networks
• Higher-order dissimilarity measures for hypergraph comparison
• Finding Influential Cores via Normalized Ricci Flows in Directed and Undirected Hypergraphs with Applications
• Adaptive behaviors neutralize bistable explosive transitions in higher-order contagion
• Higher-order adaptive behaviors outperform pairwise strategies in mitigating contagion dynamics
• The relevance of higher-order ties