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Vital node identification in hypergraphs via gravity model.

Xiaowen Xie1, Xiuxiu Zhan1, Zike Zhang2

  • 1Alibaba Research Center for Complexity Sciences, Hangzhou Normal University, Hangzhou 311121, People's Republic of China.

Chaos (Woodbury, N.Y.)
|February 1, 2023
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Summary
This summary is machine-generated.

We introduce Hypergraph Centrality (HGC), a new method for complex systems, balancing accuracy and computation. HGC effectively identifies vital nodes for connectivity and spread in hypergraph networks.

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Area of Science:

  • Complex Systems Science
  • Network Science
  • Graph Theory

Background:

  • Hypergraphs model complex systems with interactions beyond pairwise edges.
  • Centrality metrics are crucial for understanding network structures.
  • Defining centrality in hypergraphs requires utilizing higher-order structures.

Purpose of the Study:

  • To propose a novel centrality method for hypergraphs.
  • To develop a method balancing accuracy and computational complexity.
  • To introduce new metrics for evaluating hypergraph centrality.

Main Methods:

  • Proposed a Hypergraph Centrality (HGC) method based on the gravity model.
  • Developed a semi-local HGC for improved computational efficiency.
  • Introduced a complex contagion model for group influence.
  • Defined network s-efficiency based on higher-order distances.

Main Results:

  • The proposed HGC methods effectively identify nodes with high spreading ability.
  • HGC successfully filters nodes vital to hypergraph connectivity.
  • Evaluation metrics demonstrated the effectiveness of the proposed centrality methods.

Conclusions:

  • The novel HGC methods provide effective means to analyze node importance in hypergraphs.
  • Balancing accuracy and computational complexity is achievable for hypergraph centrality.
  • The developed evaluation metrics offer comprehensive insights into hypergraph dynamics.