Annotated Hypergraphs: Models and Applications

TL;DR

This paper introduces annotated hypergraphs as a flexible framework for modeling complex polyadic interactions with roles, providing new metrics, algorithms, and a null model, demonstrated on social networks including Enron emails.

Contribution

The paper develops annotated hypergraphs as a novel generalization of directed hypergraphs, along with role-aware metrics, algorithms, and a sampling scheme, advancing polyadic network analysis.

Findings

Effective role-aware null model and MCMC sampling scheme.

Generalized metrics like assortativity and modularity.

Application to social networks including Enron email data.

Abstract

Hypergraphs offer a natural modeling language for studying polyadic interactions between sets of entities. Many polyadic interactions are asymmetric, with nodes playing distinctive roles. In an academic collaboration network, for example, the order of authors on a paper often reflects the nature of their contributions to the completed work. To model these networks, we introduce \emph{annotated hypergraphs} as natural polyadic generalizations of directed graphs. Annotated hypergraphs form a highly general framework for incorporating metadata into polyadic graph models. To facilitate data analysis with annotated hypergraphs, we construct a role-aware configuration null model for these structures and prove an efficient Markov Chain Monte Carlo scheme for sampling from it. We proceed to formulate several metrics and algorithms for the analysis of annotated hypergraphs. Several of these, such as assortativity and modularity, naturally generalize dyadic counterparts. Other metrics, such as local role densities, are unique to the setting of annotated hypergraphs. We illustrate our techniques on six digital social networks, and present a detailed case-study of the Enron email data set.