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In many real-world networks the ability to synchronize is a key property for its performance. Examples include power-grid, sensor, and neuron networks as well as consensus formation. Recent work on undirected networks with diffusive…
We study the emergence of coherence in complex networks of mutually coupled non-identical elements. We uncover the precise dependence of the dynamical coherence on the network connectivity, on the isolated dynamics of the elements and the…
Most real-world networks are not isolated. In order to function fully, they are interconnected with other networks, and this interconnection influences their dynamic processes. For example, when the spread of a disease involves two species,…
Inspired by practical importance of social networks, economic networks, biological networks and so on, studies on large and complex networks have attracted a surge of attentions in the recent years. Link prediction is a fundamental issue to…
Many of the structural characteristics of a network depend on the connectivity with and within the hubs. These dependencies can be related to the degree of a node and the number of links that a node shares with nodes of higher degree. In…
Dynamical properties of complex networks are related to the spectral properties of the Laplacian matrix that describes the pattern of connectivity of the network. In particular we compute the synchronization time for different types of…
The spectral properties of the adjacency matrix provide a trove of information about the structure and function of complex networks. In particular, the largest eigenvalue and its associated principal eigenvector are crucial in the…
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…
In this article we presented a brief study of the main network models with growth and preferential attachment. Such models are interesting because they present several characteristics of real systems. We started with the classical model…
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…
The eigenvalues of matrices representing the structure of large-scale complex networks present a wide range of applications, from the analysis of dynamical processes taking place in the network to spectral techniques aiming to rank the…
Many social, technological and biological interactions involve network relationships whose outcome intimately depends on the structure of the network and on the strengths of the connections. Yet, although much information is now available…
In recent years complex networks have gained increasing attention in different fields of science and engineering. The problem of controlling these networks is an interesting and challenging problem to investigate. In this paper we look at…
We investigate the role of degree correlation among nodes on the stability of complex networks, by studying spectral properties of randomly weighted matrices constructed from directed Erd\"{o}s-R\'enyi and scale-free random graph models. We…
We characterize the large-sample properties of network modularity in the presence of covariates, under a natural and flexible nonparametric null model. This provides for the first time an objective measure of whether or not a particular…
The identification of the limiting factors in the dynamical behavior of complex systems is an important interdisciplinary problem which often can be traced to the spectral properties of an underlying network. By deriving a general relation…
The analysis of the dynamics of a large class of excitable systems on locally tree-like networks leads to the conclusion that at $\lambda=1$ a continuous phase transition takes place, where $\lambda$ is the largest eigenvalue of the…
Found in varied contexts from neurons to ants to fish, binary decision-making is one of the simplest forms of collective computation. In this process, information collected by individuals about an uncertain environment is accumulated to…
The study of complex networks has been one of the most active fields in science in recent decades. Spectral properties of networks (or graphs that represent them) are of fundamental importance. Researchers have been investigating these…
Heterogeneous networks play a key role in the evolution of communities and the decisions individuals make. These networks link different types of entities, for example, people and the events they attend. Network analysis algorithms usually…