The Laplacian tensor of a multi-hypergraph

We define a new hyper-adjacency tensor A(H)A(H) and use it to define the Laplacian L(H)L(H) and the signless Laplacian Q(H)Q(H) of a given uniform multi-hypergraph HH. We prove L(H)L(H) and Q(H)Q(H) are positive semi-definite (PSD) for connected even uniform multigraphs. Some analyses on the largest and smallest HH and ZZ-eigenvalues of L(H)L(H) are given as well as a comparison of other adjacency tensors.