Uniqueness of weighted network equivalents for weighted hypergraphs

Determine whether a weighted hypergraph has a unique equivalent weighted network, and establish whether such an equivalence is useful beyond the construction of Laplacians.

Background

The manuscript asks whether weighted hypergraph structures admit a unique representation as weighted networks, referring specifically to the correspondence discussed in Carletti et al.'s work on dynamical systems on hypergraphs. It also asks whether this correspondence has applications beyond Laplacian operators, indicating an unresolved representational and methodological issue.