Related papers: The multiplex decomposition: An analytic framework…

The multilayer network framework has served to describe and uncover a number of novel and unforeseen physical behaviors and regimes in interacting complex systems. However, the majority of existing studies are built on undirected multilayer…

Real-world complex systems exhibit multiple levels of relationships. In many cases, they require to be modeled by interconnected multilayer networks, characterizing interactions on several levels simultaneously. It is of crucial importance…

The stability (or instability) of synchronization is important in a number of real world systems, including the power grid, the human brain and biological cells. For identical synchronization, the synchronizability of a network, which can…

One of the reasons behind the success of Social Network Analysis is its simple and general graph model made of nodes (representing individuals) and ties. However, when we focus on our daily on-line experience we must confront a more complex…

Modular structure is ubiquitous among complex networks. We note that most such systems are subject to multiple structural and functional constraints, e.g., minimizing the average path length and the total number of links, while maximizing…

Multiplex graphs capture diverse relations among shared nodes. Most predictors either collapse layers or treat them independently. This loses crucial inter-layer dependencies and struggles with scalability. To overcome this, we frame…

Understanding how different networks relate to each other is key for obtaining a greater insight into complex systems. Here, we introduce an intuitive yet powerful framework to characterise the relationship between two networks comprising…

Community structures in collaboration networks reflect the natural tendency of individuals to organize their work in groups in order to better achieve common goals. In most of the cases, individuals exploit their connections to introduce…

Recent developments of the multiplex paradigm included efforts to understand the role played by the presence of several layers on the dynamics of processes running on these networks. The possible existence of new phenomena associated to the…

Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…

Different aspects of synchronization emerging in dynamical networks of coupled oscillators have been examined prominently in the last decades. Nevertheless, little attention has been paid on the emergence of this imperative collective…

Stabilizing large networks of nonlinear agents is challenging; decomposition and distributed analysis of these networks are crucial for computational tractability and information security. Vidyasagar's Network Dissipativity Theorem enables…

Time lags occur in a vast range of real-world dynamical systems due to finite reaction times or propagation speeds. Here we derive an analytical approach to determine the asymptotic stability of synchronous states in networks of coupled…

We show that subsets of interacting oscillators may synchronize in different ways within a single network. This diversity of synchronization patterns is promoted by increasing the heterogeneous distribution of coupling weights and/or…

Network embedding is an effective technique to learn the low-dimensional representations of nodes in networks. Real-world networks are usually with multiplex or having multi-view representations from different relations. Recently, there has…

Complex systems are characterized by multiple spatial and temporal scales. A natural framework to capture their multiscale nature is that of multilayer networks, where different layers represent distinct physical processes that often…

Many real-world network are multilayer, with nontrivial correlations across layers. Here we show that these correlations amplify geometry in networks. We focus on mutual clustering--a measure of the amount of triangles that are present in…

We investigate spatio-temporal patterns occurring in a two-layer multiplex network of oscillatory FitzHugh-Nagumo neurons, where each layer is represented by a nonlocally coupled ring. We show that weak multiplexing, i.e., when the coupling…

The dynamics and the stationary states of an exactly solvable three-state layered feed-forward neural network model with asymmetric synaptic connections, finite dilution and low pattern activity are studied in extension of a recent work on…

Multilayer networks provide a more comprehensive framework for exploring real-world and engineering systems than traditional single-layer networks, consisting of multiple interacting networks. However, despite significant research in…