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We introduce a method that can be used to evolve the topology of a network in a way that preserves both the network's spectral as well as local structure. This method is quite versatile in the sense that it can be used to evolve a network's…

Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical…

The human organism is an integrated network where complex physiologic systems, each with its own regulatory mechanisms, continuously interact, and where failure of one system can trigger a breakdown of the entire network. Identifying and…

Complex systems are characterized by many interacting units that give rise to emergent behavior. A particularly advantageous way to study these systems is through the analysis of the networks that encode the interactions among the system's…

The increasing volume of ecologically and biologically relevant data has revealed a wide collection of emergent patterns in living systems. Analyzing different datasets, ranging from metabolic gene-regulatory to species interaction…

Dynamic networks consist of interconnected dynamical systems. The subsystems can be viewed as transformations of input signals into output signals, where signals flow from one system into another through interconnections. The signal flows…

Percolation, the formation of a macroscopic connected component, is a key feature in the description of complex networks. The dynamical properties of a variety of systems can be understood in terms of percolation, including the robustness…

Driven by growing interest in the sciences, industry, and among the broader public, a large number of empirical studies have been conducted in recent years of the structure of networks ranging from the internet and the world wide web to…

We study the stability of the dynamics of a network of n neurons intercting linearly through a random gaussian matrix of excitatory and inhibitory type. Using the aproach developed in a previous paper we show some interesting properties of…

Various approaches and measures from network analysis have been applied to granular and particulate networks to gain insights into their structural, transport, failure-propagation and other systems-level properties. In this article, we…

A fundamental premise of statistical physics is that the particles in a physical system are interchangeable, and hence the state of each specific component is representative of the system as a whole. This assumption breaks down for complex…

Turing patterns formed by activator-inhibitor systems on networks are considered. The linear stability analysis shows that the Turing instability generally occurs when the inhibitor diffuses sufficiently faster than the activator. Numerical…

Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network structure does not entail that the brain actually works as a network. Asking whether the…

We study numerically the dynamics of a network of all-to-all-coupled, identical sub-networks consisting of diffusively coupled, non-identical FitzHugh--Nagumo oscillators. For a large range of within- and between-network couplings, the…

Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…

Over the last years, a great deal of attention has been focused on complex networked systems, characterized by intricate structure and dynamics. The latter has been often represented in terms of overall statistics (e.g. average and standard…

Scale-free and non-computable characteristics of natural networks are found to result from the least-time dispersal of energy. To consider a network as a thermodynamic system is motivated since ultimately everything that exists can be…

Diffusion dynamics in multiplex networks can model a diverse number of real-world processes. In some specific configurations of these systems, the super-diffusion phenomenon arises, in which the diffusion is faster in the multiplex network…

Threshold-linear networks consist of simple units interacting in the presence of a threshold nonlinearity. Competitive threshold-linear networks have long been known to exhibit multistability, where the activity of the network settles into…

Traditional mathematical approaches to studying analytically the dynamics of neural networks rely on the mean-field approximation, which is rigorously applicable only to networks of infinite size. However, all existing real biological…