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We investigate the effects of structural perturbations of both, undirected and directed diffusive networks on their ability to synchronize. We establish a classification of directed links according to their impact on synchronizability. We…

The relation between network structure and dynamics is determinant for the behavior of complex systems in numerous domains. An important long-standing problem concerns the properties of the networks that optimize the dynamics with respect…

We study synchronization and consensus in a group of dynamical systems coupled via multiple directed networks. We show that even though the coupling in a single network may not be sufficient to synchronize the systems, combination of…

The lack of studying the complex organization of directed network usually limits to the understanding of underlying relationship between network structures and functions. Structural controllability and structural predictability, two…

In this Letter we identify the general rules that determine the synchronization properties of interconnected networks. We study analytically, numerically and experimentally how the degree of the nodes through which two networks are…

Directionality is a fundamental feature of network connections. Most structural brain networks are intrinsically directed because of the nature of chemical synapses, which comprise most neuronal connections. Due to limitations of…

Networks are universally considered as complex structures of interactions of large multi-component systems. In order to determine the role that each node has inside a complex network, several centrality measures have been developed. Such…

Current network models assume one type of links to define the relations between the network entities. However, many real networks can only be correctly described using two different types of relations. Connectivity links that enable the…

A given neural network in the brain is involved in many different tasks. This implies that, when considering a specific task, the network's connectivity contains a component which is related to the task and another component which can be…

The control of complex networks is of paramount importance in areas as diverse as ecosystem management, emergency response, and cell reprogramming. A fundamental property of networks is that perturbations to one node can affect other nodes,…

Synchrony is one of the most common dynamical states emerging on networks. The speed of convergence towards synchrony provides a fundamental collective time scale for synchronizing systems. Here we study the asymptotic synchronization times…

Experimental results often do not assess network structure; rather, the network structure is inferred by the dynamics of the nodes. From the dynamics of the nodes one then constructs a network of functional relations, termed the functional…

Synchronization, in which individual dynamical units keep in pace with each other in a decentralized fashion, depends both on the dynamical units and on the properties of the interaction network. Yet, the role played by the network has…

Symmetries are ubiquitous in network systems and have profound impacts on the observable dynamics. At the most fundamental level, many synchronization patterns are induced by underlying network symmetry, and a high degree of symmetry is…

In this paper, the relationship between the network synchronizability and the edge distribution of its associated graph is investigated. First, it is shown that adding one edge to a cycle definitely decreases the network sychronizability.…

The study of network synchronization has attracted increasing attention recently. In this paper, we strictly define a class of networks, namely effective networks, which are synchronizable and orientable networks. We can prove that all the…

Most real-world networks display not only a heterogeneous distribution of degrees, but also a heterogeneous distribution of weights in the strengths of the connections. Each of these heterogeneities alone has been shown to suppress…

In this paper, the investigation is first motivated by showing two examples of simple regular symmetrical graphs, which have the same structural parameters, such as average distance, degree distribution and node betweenness centrality, but…

Synchronization phenomena on networks have attracted much attention in studies of neural, social, economic, and biological systems, yet we still lack a systematic understanding of how relative synchronizability relates to underlying network…

Natural and man-made networks often possess locally tree-like sub-structures. Taking such tree networks as our starting point, we show how the addition of links changes the synchronization properties of the network. We focus on two…