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

Marco Mancastroppa1, Iacopo Iacopini2,3, Giovanni Petri2,4

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Summary
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This study introduces hyper-cores and hypercoreness to analyze complex systems represented as hypergraphs. Nodes with high hypercoreness exhibit significant spreading power in higher-order dynamics and social convention emergence.

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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.