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 hypercoreness. We assess the role of hyper-cores and nodes with large hypercoreness 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 hypercoreness 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.

Legal hypergraphs

“…In higher-order network science, much work has been done to port concepts and methods from graphs to hypergraphs, leading, e.g. to generalizations of walks [50,51], centralities [52,53], motifs [12,[54][55][56], clustering [57][58][59][60] and cores [61]. Exploiting edge cardinality as a new source Table 1.…”

“…In higher-order network science , much work has been done to port concepts and methods from graphs to hypergraphs , leading, e.g. to generalizations of walks [ 50 , 51 ], centralities [ 52 , 53 ], motifs [ 12 , 54 – 56 ], clustering [ 57 – 60 ] and cores [ 61 ]. Exploiting edge cardinality as a new source of variation in hypergraphs, researchers are increasingly adapting concepts and methods from topology to analyse higher-order network data [ 13 , 62 , 63 ], and they have also made some progress by leveraging (structurally more constrained) simplicial complexes [ 64 – 67 ].…”