Clustering coefficient reflecting pairwise relationships within hyperedges.

Area of Science:

• Network Science
• Graph Theory
• Data Analysis

Background:

• Hypergraphs model complex group interactions beyond simple pairwise relationships.
• Existing hypergraph clustering coefficients fail to capture intra-hyperedge relationships, leading to inaccurate density measurements.

Purpose of the Study:

• To propose a novel hypergraph clustering coefficient that accurately quantifies local link density.
• To address the limitations of existing methods in capturing intra-hyperedge pairwise relationships.

Main Methods:

• Transforming hypergraphs into weighted graphs to represent relationship strength.
• Developing a new definition for hypergraph clustering coefficients.

Main Results:

• The proposed coefficient yields values in the range [0,1] and is consistent with simple graph coefficients.
• It accurately captures intra-hyperedge pairwise relationships, unlike existing definitions.
• Theoretical and empirical evaluations show improved accuracy, especially for larger hyperedges.

Conclusions:

• The novel clustering coefficient offers a more accurate quantification of local density in complex networks.
• It reveals structural characteristics missed by previous definitions in systems with group memberships.