Eigenvector centrality in simplicial complexes of hypergraphs
1School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan 250014, People's Republic of China.
Chaos (Woodbury, N.Y.)
|September 8, 2023
Summary
This study introduces Simplicial DualRank centrality, a novel method for identifying vital nodes in hypergraphs by analyzing their simplicial complex structure. This approach enhances understanding of complex networks and collaboration patterns.
Area of Science:
- Network Science
- Graph Theory
- Data Analysis
Background:
- Hypergraphs model complex relationships within clustered objects.
- Identifying crucial nodes is essential for hypergraph analysis.
- Existing methods may not fully capture multilayered hypergraph features.
Purpose of the Study:
- To develop a new centrality measure for weighted hypergraphs.
- To analyze homological dual relations within hypergraphs.
- To provide a global framework for hypergraph exploration.
Main Methods:
- Deconstructing hypergraphs into simplicial complexes.
- Analyzing boundary and coboundary relations between simplices.
- Developing Simplicial DualRank centrality based on inner and outer centrality indices.
Main Results:
- A parameter-free eigenvector centrality for weighted hypergraphs was proposed.
- The Simplicial DualRank centrality was defined via a circuit on the simplicial diagram.
- Application to weighted complex networks yielded a variant of eigenvector centrality.
Conclusions:
- Simplicial DualRank can identify key figures, like Nobel laureates, in scientific collaborations.
- The method highlights the importance of careful collaborator selection for research quality.
- It suggests scholars can find effective future collaborations using this analysis.
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