  Statistical analysis and node clustering in hypergraphs constitute an
emerging topic suffering from a lack of standardization. In contrast to the
case of graphs, the concept of nodes' community in hypergraphs is not unique
and encompasses various distinct situations. In this work, we conducted a
comparative analysis of the performance of modularity-based methods for
clustering nodes in binary hypergraphs. To address this, we begin by
presenting, within a unified framework, the various hypergraph modularity
criteria proposed in the literature, emphasizing their differences and
respective focuses. Subsequently, we provide an overview of the
state-of-the-art codes available to maximize hypergraph modularities for
detecting node communities in binary hypergraphs. Through exploration of
various simulation settings with controlled ground truth clustering, we offer a
comparison of these methods using different quality measures, including true
clustering recovery, running time, (local) maximization of the objective, and
the number of clusters detected. Our contribution marks the first attempt to
clarify the advantages and drawbacks of these newly available methods. This
effort lays the foundation for a better understanding of the primary objectives
of modularity-based node clustering methods for binary hypergraphs.
