Generative hypergraph clustering: From blockmodels to modularity.

Area of Science:

• Network Science
• Data Mining
• Computational Social Science

Background:

• Hypergraphs are essential for modeling systems with multiway interactions, unlike traditional graphs that represent pairwise relationships.
• Identifying densely interconnected nodes (clustering) is a fundamental challenge in network analysis.

Purpose of the Study:

• To propose a probabilistic generative model for clustered hypergraphs with varying node degrees and edge sizes.
• To develop clustering algorithms that generalize existing graph community detection methods, such as modularity optimization and the Louvain method.

Main Methods:

• Developed a probabilistic generative model for clustered hypergraphs.
• Derived an approximate maximum likelihood inference approach, generalizing graph modularity.
• Adapted the Louvain algorithm for hypergraph clustering and introduced a specialized, faster variant.

Main Results:

• The proposed hypergraph clustering method generalizes graph-based objectives and algorithms.
• A specialized variant demonstrates high scalability and effectiveness in detecting clusters missed by graph methods.
• Successfully applied the model to diverse real-world datasets, including social networks, legislative data, and e-commerce behavior.

Conclusions:

• The developed hypergraph clustering framework provides a powerful tool for analyzing complex, multiway interactions.
• The specialized algorithm offers a scalable solution for uncovering higher-order structures in large networks.
• The approach reveals interpretable patterns in various empirical domains, advancing network analysis capabilities.