Characterize mixed graphs arising from hypergraph adjacency matrices

Characterize the mixed graphs whose adjacency matrices arise from hypergraphs under the characteristic adjacency-matrix construction.

Background

The paper associates a mixed graph G_H with each hypergraph H by interpreting the characteristic adjacency matrix A_H as a mixed-digraph adjacency matrix. Although the construction maps every hypergraph to such a mixed graph, the converse characterization is left unresolved: the paper asks which mixed graphs can be obtained in this way. This is a recognition or realizability problem for the class of mixed graphs induced by hypergraphs.