Identifying clique influences in hypergraphs via the simplicial complex with applications in scientific...

Area of Science:

• Network analysis
• Hypergraph theory
• Complex systems

Background:

• Hypergraphs are crucial for modeling higher-order structures in networks.
• Existing network analysis methods often struggle with complex hypergraph structures.
• There is a need for robust centrality measures applicable to diverse hypergraphs.

Purpose of the Study:

• To propose a parameter-free clique centrality index for all hypergraphs.
• To introduce the Hereditary DualRank centrality measure.
• To analyze collaboration patterns in scientific research using the new index.

Main Methods:

• Construction of a hereditary class within the simplicial complex of a hypergraph.
• Definition of inner and outer centrality indices based on boundary-coboundary relations.
• Development of the Hereditary DualRank centrality from a global circuit's steady state.
• Calculation of simplex effectiveness and collaboration efficiency indices.

Main Results:

• The Hereditary DualRank centrality is defined for all simplices in any hypergraph.
• Effectiveness index quantifies the productivity of cliques.
• Analysis of a scientific collaboration dataset reveals scholars' preference for effective cooperation.
• Collaboration efficiency shows a negative correlation with the dispersity of individual effectiveness.

Conclusions:

• Hereditary DualRank centrality provides a novel topological understanding of hypergraphs.
• The effectiveness and efficiency indices offer insights into collaboration dynamics.
• This framework enhances the analysis of complex network evolution and decision-making processes.