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

Area of Science:

• Complex Systems Science
• Network Science
• Data Analysis

Background:

• Traditional network analysis struggles with higher-order interactions.
• Describing complex systems requires methods beyond pairwise connections.
• Tools for analyzing hypergraph structures and central nodes are limited.

Purpose of the Study:

• To introduce a novel decomposition method for hypergraphs called hyper-cores.
• To propose a new centrality measure, hypercoreness, for hypergraphs.
• To investigate the role of hyper-cores and hypercoreness in higher-order dynamics and social convention emergence.

Main Methods:

• Decomposition of hypergraphs into hyper-cores based on hyperedge size and count.
• Introduction and calculation of the hypercoreness centrality measure.
• Assessment of hyper-cores and hypercoreness in higher-order dynamical processes and social convention modeling.

Main Results:

• Hyper-core decomposition provides a fingerprint for hypergraph data.
• Nodes with high hypercoreness demonstrate significant spreading power.
• Spreading processes are localized within central hyper-cores.
• Few individuals with high hypercoreness can influence social convention shifts.

Conclusions:

• Hyper-cores and hypercoreness offer valuable tools for analyzing complex systems represented by hypergraphs.
• This framework enhances understanding of higher-order dynamics and social phenomena.
• Opens avenues for empirical data comparison, model validation, and temporal hypergraph studies.