In this chapter we discuss the spectral theory of discrete structures such as graphs, simplicial
complexes and hypergraphs. We focus, in particular, on the corresponding Laplace …

Several new spectral properties of the normalized Laplacian defined for oriented
hypergraphs are shown. The eigenvalue 1 and the case of duplicate vertices are discussed; …

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In this article, we define signless Laplacian matrix of a hypergraph and obtain structural
properties from its eigenvalues. We generalize several known results for graphs, relating the …

An oriented hypergraph is an oriented incidence structure that allows for the generalization
of graph theoretic concepts to integer matrices through its locally signed graphic …

Here, we represent a general hypergraph by a matrix and study its spectrum. We extend the
definition of equitable partition and joining operation for hypergraphs, and use those to …

The independence number, coloring number and related parameters are investigated in the
setting of oriented hypergraphs using the spectrum of the normalized Laplace operator. For …

Chemical hypergraphs and their associated normalized Laplace operators are generalized
and studied in the case where each vertex–hyperedge incidence has a real coefficient. We …

For a square matrix M, its energy E (M) is the sum of its singular values. Let H be a k-uniform
hypergraph, and let B (H) be the incidence matrix of H. The incidence energy BE (H) of H is …

In this paper, we define and obtain several properties of the (adjacency) energy of a
hypergraph. In particular, bounds for this energy are obtained as functions of structural and …