Community detection in hypergraphs through hyperedge percolation

Area of Science:

• Network Science
• Graph Theory
• Data Mining

Background:

• Complex networks often display community structure, where nodes are densely interconnected within groups.
• Modeling systems with interactions involving more than two nodes requires hypergraphs, necessitating specialized community detection algorithms.

Purpose of the Study:

• To adapt the k-clique percolation method for community detection in hypergraphs.
• To explore two distinct hypergraph community detection algorithms and compare their performance.

Main Methods:

• Adapted k-clique percolation to hypergraphs by defining communities based on hyperedges with at least k nodes.
• Proposed an alternative method restricting maximum hyperedge size for community detection.
• Compared algorithms on synthetic and real-world hypergraphs, including those from hyperbolic geometry.

Main Results:

• Communities detected directly from hyperedges can differ from those found using the pairwise projection of the hypergraph.
• The alternative method, restricting maximum hyperedge size, is more suitable for hypergraphs with weaker linkages represented by larger hyperedges.

Conclusions:

• The proposed hypergraph community detection methods provide valuable tools for analyzing complex systems.
• The choice of algorithm depends on the specific characteristics of the hypergraph, particularly hyperedge cardinality and linkage strength.