Over the last 20 years networks have emerged as the paradigmatic framework to model
complex systems. Yet, as simple collections of nodes and links, they are intrinsically limited …

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; …

We develop a general theory of random walks on hypergraphs which includes, as special
cases, the different models that are found in literature. In particular, we introduce and …

The p-Laplacian for graphs, as well as the vertex Laplace operator and the hyperedge
Laplace operator for the general setting of oriented hypergraphs, are generalized. In …

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 …

The spectral theory of the normalized Laplacian for chemical hypergraphs is further
investigated. The signless normalized Laplacian is introduced and it is shown that its …

The graph Cheeger constant and Cheeger inequalities are generalized to the case of
hypergraphs whose edges have the same cardinality. In particular, it is shown that the …

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