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 …

Spectral methods offer a tractable, global framework for clustering in graphs via eigenvector
computations on graph matrices. Hypergraph data, in which entities interact on edges of …

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 …

We develop a model-independent reduction method of chemical reaction systems based on
the stoichiometry, which determines their network topology. A subnetwork can be eliminated …

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 …

One way to study a hypergraph is to attach to it a tensor. Tensors are a generalization of
matrices, and they are an efficient way to encode information in a compact form. In this …

Multiplex networks describe systems whose interactions can be of different nature, and are
fundamental to understand complexity of networks beyond the framework of simple graphs …

In this work we describe how to systematically implement a full graph decomposition to set
up a linked-cluster expansion for the topological phase of Kitaev's toric code in a field. This …

In order to increase the accuracy of ocean monitoring, this paper proposes an improved
adaptive median filtering algorithm based on the tangential interference ratio to better …

We have established a coherent framework for applying variational methods to partial
differential equations on hypergraphs, which includes the propositions of calculus and …