  Conventional network data has largely focused on pairwise interactions
between two entities, yet multi-way interactions among multiple entities have
been frequently observed in real-life hypergraph networks. In this article, we
propose a novel method for detecting community structure in general hypergraph
networks, uniform or non-uniform. The proposed method introduces a null vertex
to augment a non-uniform hypergraph into a uniform multi-hypergraph, and then
embeds the multi-hypergraph in a low-dimensional vector space such that
vertices within the same community are close to each other. The resultant
optimization task can be efficiently tackled by an alternative updating scheme.
The asymptotic consistencies of the proposed method are established in terms of
both community detection and hypergraph estimation, which are also supported by
numerical experiments on some synthetic and real-life hypergraph networks.
