Related papers: Dynamical complexity as a proxy for the network de…

The concept of entropy rate for a dynamical process on a graph is introduced. We study diffusion processes where the node degrees are used as a local information by the random walkers. We describe analitically and numerically how the degree…

We introduce the concept of control centrality to quantify the ability of a single node to control a directed weighted network. We calculate the distribution of control centrality for several real networks and find that it is mainly…

Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…

In this paper, we study instances of complex neural networks, i.e. neural netwo rks with complex topologies. We use Self-Organizing Map neural networks whose n eighbourhood relationships are defined by a complex network, to classify handwr…

We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…

While the majority of approaches to the characterization of complex networks has relied on measurements considering only the immediate neighborhood of each network node, valuable information about the network topological properties can be…

In spite of a few attempts in understanding the dynamical robustness of complex networks, this extremely important subject of research is still in its dawn as compared to the other dynamical processes on networks. We hereby consider the…

Biological networks have been recently found to exhibit many topological properties of the so-called complex networks. It has been reported that they are, in general, both highly skewed and directed. In this paper, we report on the dynamics…

The network density matrix formalism allows for describing the dynamics of information on top of complex structures and it has been successfully used to analyze from system's robustness to perturbations to coarse graining multilayer…

In this paper, we study the crucial elements of complex networks, namely nodes, and edges and their properties such as their community structure, which play an important role in dictating the robustness of the network towards structural…

The problem of controllability of the dynamical state of a network is central in network theory and has wide applications ranging from network medicine to financial markets. The driver nodes of the network are the nodes that can bring the…

The goal of is to study how increased variability in the degree distribution impacts the global connectivity properties of a large network. We approach this question by modeling the network as a uniform random graph with a given degree…

Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior…

We study the synchronization of coupled dynamical systems on a variety of networks. The dynamics is governed by a local nonlinear map or flow for each node of the network and couplings connecting different nodes via the links of the…

The collective dynamics of a network of coupled excitable systems in response to an external stimulus depends on the topology of the connections in the network. Here we develop a general theoretical approach to study the effects of network…

We investigate to what extent the degree sequence of a directed network constrains the number of driver nodes. We develop a pair of algorithms that take a directed degree sequence as input and aim to output a network with the maximum or…

The structure of a complex network plays a crucial role in determining its dynamical properties. In this work, we show that the the degree to which a network is directed and hierarchically organised is closely associated with the degree to…

Dynamic networks are structured interconnections of dynamical systems (modules) driven by external excitation and disturbance signals. In order to identify their dynamical properties and/or their topology consistently from measured data, we…

Network topology is a fundamental aspect of network science that allows us to gather insights into the complicated relational architectures of the world we inhabit. We provide a first specific study of neighbourhood degree sequences in…

While interdependent systems have usually been associated with increased fragility, we show that strengthening the interdependence between dynamical processes on different networks can make them more robust. By coupling the dynamics of…