Related papers: Correlations between thresholds and degrees: An an…
We analyze a minimal model of a growing network. At each time step, a new vertex is added; then, with probability delta, two vertices are chosen uniformly at random and joined by an undirected edge. This process is repeated for t time…
Scale-free networks, in which the distribution of the degrees obeys a power-law, are ubiquitous in the study of complex systems. One basic network property that relates to the structure of the links found is the degree assortativity, which…
It appeared recently that the underlying degree distribution of networks may play a crucial role concerning their robustness. Empiric and analytic results have been obtained, based on asymptotic and mean-field approximations. Previous work…
Network controllability robustness reflects how well a networked dynamical system can maintain its controllability against destructive attacks. This paper investigates the network controllability robustness from the perspective of a…
We discuss two sampling schemes for selecting random subnets from a network: Random sampling and connectivity dependent sampling, and investigate how the degree distribution of a node in the network is affected by the two types of sampling.…
Understanding the evolution of cooperation in structured populations represented by networks is a problem of long research interest, and a most fundamental and widespread property of social networks related to cooperation phenomena is that…
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…
In the study of infectious diseases on networks, researchers calculate epidemic thresholds to help forecast whether a disease will eventually infect a large fraction of a population. Because network structure typically changes in time,…
The existence or not of a percolation threshold on power law correlated graphs is a fundamental question for which a general criterion is lacking. In this work we investigate the problems of site and bond percolation on graphs with degree…
Cascading failures are a critical vulnerability of complex information or infrastructure networks. Here we investigate the properties of load-based cascading failures in real and synthetic spatially-embedded network structures, and propose…
A model of correlated random networks is examined, i.e. networks with correlations between the degrees of neighboring nodes. These nodes do not necessarily have to be direct neighbors, the maximum range of the correlations can be…
We explore the relation between the topological relevance of a node in a complex network and the individual dynamics it exhibits. When the system is weakly coupled, the effect of the coupling strength against the dynamical complexity of the…
Epidemiological contact network models have emerged as an important tool in understanding and predicting the spread of infectious disease, due to their capacity to engage individual heterogeneity that may underlie essential dynamics of a…
We derive mean-field equations that describe the dynamics of a general model of rumor spreading on complex networks, and use analytical and numerical solutions of these equations to examine the threshold behavior and dynamics of the model…
In heterogeneous network systems such as ecological and social networks, structural stability depends on how connectivity changes under node removal, as different removal sequences can trigger distinct modes of systemic collapse. While…
The spread of a disease, a computer virus or information is discussed in a directed complex network. We are concerned with a steady state of the spread for the SIR and SIS dynamic models. In a scale-free directed network it is shown that…
Contagions such as the spread of popular news stories, or infectious diseases, propagate in cascades over dynamic networks with unobservable topologies. However, "social signals" such as product purchase time, or blog entry timestamps are…
Yang, Wang, and Motter [Phys. Rev. Lett. 109, 258701 (2012)] analyzed a model for network observability transitions in which a sensor placed on a node makes the node and the adjacent nodes observable. The size of the connected components…
We study the synchronization transition in scale-free networks that display power-law asymptotic behaviors in their degree distributions. The critical coupling strength and the order-parameter critical exponent derived by the mean field…
This article discusses the properties of extremes of degree sequences calculated from network data. We introduce the notion of a normalized degree, in order to permit a comparison of degree sequences between networks with differing numbers…