Related papers: Spreading on a complex network avoiding certain mo…

We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model and, by performing percolation processes, we get information about topology and resilience properties of the networks…

How an information spreads throughout a social network is a valuable knowledge sought by many groups such as marketing enterprises and political parties. If they can somehow predict the impact of a given message or manipulate it in order to…

We study the effects of nonreciprocity and network structure on percolation. To this end, we investigate nonreciprocal random networks - directed networks for which the probability of a link occurring from node i to node j differs from the…

Classical percolation theory underlies many processes of information transfer along the links of a network. In these standard situations, the requirement for two nodes to be able to communicate is the presence of at least one uninterrupted…

We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…

Optimal percolation is the problem of finding the minimal set of nodes such that if the members of this set are removed from a network, the network is fragmented into non-extensive disconnected clusters. The solution of the optimal…

Most networks of interest do not live in isolation. Instead they form components of larger systems in which multiple networks with distinct topologies coexist and where elements distributed amongst different networks may interact directly.…

Connectivity correlations play an important role in the structure of scale-free networks. While several empirical studies exist, there is no general theoretical analysis that can explain the largely varying behavior of real networks. Here,…

Spreading phenomena are ubiquitous in nature and society. For example, disease, rumor, and information spread over underlying social and information networks. It is well known that there is no threshold for epidemic models on scale-free…

Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…

The Internet, as well as many other networks, has a very complex connectivity recently modeled by the class of scale-free networks. This feature, which appears to be very efficient for a communications network, favors at the same time the…

We introduce a general stochastic model for the spread of rumours, and derive mean-field equations that describe the dynamics of the model on complex social networks (in particular those mediated by the Internet). We use analytical and…

Quantum networks are essential to quantum information distributed applications, and communicating over them is a key challenge. Complex networks have rich and intriguing properties, which are as yet unexplored in the quantum setting. Here,…

We develop a theoretical approach to percolation in random clustered networks. We find that, although clustering in scale-free networks can strongly affect some percolation properties, such as the size and the resilience of the giant…

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…

Complex networks are now being studied in a wide range of disciplines across science and technology. In this paper we propose a method by which one can probe the properties of experimentally obtained network data. Rather than just measuring…

The inverse problem of finding the optimal network structure for a specific type of dynamical process stands out as one of the most challenging problems in network science. Focusing on the susceptible-infected-susceptible type of dynamics…

There has been a considerable amount of interest in recent years on the robustness of networks to failures. Many previous studies have concentrated on the effects of node and edge removals on the connectivity structure of a static network;…

In this paper, we give an analytic solution for graphs with n nodes and E edges for which the probability of obtaining a given graph G is specified in terms of the degree sequence of G. We describe how this model naturally appears in the…

We study the statistical properties of large random networks with specified degree distributions. New techniques are presented for analyzing the structure of social networks. Specifically, we address the question of how many nodes exist at…