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We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows the for the generation of…

Multilayer networks preserve full information about the different interactions among the constituents of a complex system, and have recently proven quite useful in modelling transportation networks, social circles, and the human brain. A…

Simplicial complexes describe collaboration networks, protein interaction networks and brain networks and in general network structures in which the interactions can include more than two nodes. In real applications, often simplicial…

A wide variety of complex systems are characterized by interactions of different types involving varying numbers of units. Multiplex hypergraphs serve as a tool to describe such structures, capturing distinct types of higher-order…

Large-scale quantum networks have been employed to overcome practical constraints of transmissions and storage for single entangled systems. Our goal in this article is to explore the strong entanglement distribution of quantum networks. We…

This chapter provides a comprehensive and self-contained discussion of the most recent developments of information theory of networks. Maximum entropy models of networks are the least biased ensembles enforcing a set of constraints and are…

Quantum network is a set of nodes connected with channels, through which the nodes communicate photons and classical information. Classical structural complexity of a quantum network may be defined through its physical structure, i.e.…

Diffusion describes the motion of microscopic entities from regions of high concentration to regions of low concentration. In multiplex networks, flows can occur both within and across layers, and super-diffusion, a regime where the time…

A geometric entropy is defined as the Riemannian volume of the parameter space of a statistical manifold associated with a given network. As such it can be a good candidate for measuring networks complexity. Here we investigate its ability…

We derive Bose-Einstein statistics and Fermi-Dirac statistics by Principle of Maximum Entropy applied to two families of entropy functions different from the Boltzmann-Gibbs-Shannon entropy. These entropy functions are identified with…

From transportation networks to complex infrastructures, and to social and economic networks, a large variety of systems can be described in terms of multiplex networks formed by a set of nodes interacting through different network layers.…

Recently much attention has been paid to the study of the robustness of interdependent and multiplex networks and, in particular, networks of networks. The robustness of interdependent networks can be evaluated by the size of a mutually…

Higher-order networks are gaining significant scientific attention due to their ability to encode the many-body interactions present in complex systems. However, higher-order networks have the limitation that they only capture many-body…

It has been recognized that many complex dynamical systems in the real world require a description in terms of multiplex networks, where a set of common, mutually connected nodes belong to distinct network layers and play a different role…

In this paper, we develop a blended dynamics framework for open quantum networks with diffusive couplings. The network consists of qubits interconnected through Hamiltonian couplings, environmental dissipation, and consensus-like diffusive…

Synchrony patterns describe network states in which nodes of a coupled dynamical system are grouped into clusters based on synchronization between nodes. Beyond simple synchrony, synchronized clusters may also exhibit active or inactive…

This research establishes that many real-world networks exhibit bounded expansion, a strong notion of structural sparsity, and demonstrates that it can be leveraged to design efficient algorithms for network analysis. We analyze several…

Many real complex systems cannot be represented by a single network, but due to multiple sub-systems and types of interactions, must be represented as a multiplex network. This is a set of nodes which exist in several layers, with each…

The rapidly developing theory of complex networks indicates that real networks are not random, but have a highly robust large-scale architecture, governed by strict organizational principles. Here, we focus on the properties of biological…

What do societies, the Internet, and the human brain have in common? They are all examples of complex relational systems, whose emerging behaviours are largely determined by the non-trivial networks of interactions among their constituents,…