Combining directed-hypergraph matrix notions with signed weights

Determine how incidence matrices, adjacency matrices, and Laplacians for directed hypergraphs can be combined consistently when hyperedge weights have arbitrary signs.

Background

After discussing positive-weight directed hypergraphs, the manuscript raises the unresolved issue of extending the relevant matrix constructions to arbitrary signed weights. The problem concerns how to preserve coherent direction and sign conventions when defining incidence-based adjacency and Laplacian operators.