相关论文: Percolation in networks composed of connectivity a…

Two stochastic models are proposed to generate a system composed of two interdependent scale-free (SF) or Erd\H{o}s-R\'{e}nyi (ER) networks where interdependent nodes are connected with exponential or power-law relation, as well as…

We study a problem of failure of two interdependent networks in the case of correlated degrees of mutually dependent nodes. We assume that both networks (A and B) have the same number of nodes $N$ connected by the bidirectional dependency…

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…

We provide arguments for the property of the degree-degree correlations of giant components formed by the percolation process on uncorrelated random networks. Using the generating functions, we derive a general expression for the…

In interdependent networks, it is usually assumed, based on percolation theory, that nodes become nonfunctional if they lose connection to the network giant component. However, in reality, some nodes, equipped with alternative resources,…

We introduce a growing network model---the copying model---in which a new node attaches to a randomly selected target node and, in addition, independently to each of the neighbors of the target with copying probability $p$. When…

Modeling how networks change under structural perturbations can yield foundational insights into network robustness, which is critical in many real-world applications. The largest connected component is a popular measure of network…

Robustness of two coupled networks system has been studied only for dependency coupling (S. Buldyrev et. al., Nature, 2010) and only for connectivity coupling (E. A. Leicht and R. M. D'Souza, arxiv:09070894). Here we study, using a…

Clustering, or transitivity has been observed in real networks and its effects on their structure and function has been discussed extensively. The focus of these studies has been on clustering of single networks while the effect of…

We give an exact solution for the complete distribution of component sizes in random networks with arbitrary degree distributions. The solution tells us the probability that a randomly chosen node belongs to a component of size s, for any…

The entropy of network ensembles characterizes the amount of information encoded in the network structure, and can be used to quantify network complexity, and the relevance of given structural properties observed in real network datasets…

We study a system composed from two interdependent networks A and B, where a fraction of the nodes in network A depends on the nodes of network B and a fraction of the nodes in network B depends on the nodes of network A. Due to the…

Real networks are vulnerable to random failures and malicious attacks. However, when a node is harmed or damaged, it may remain partially functional, which helps to maintain the overall network structure and functionality. In this paper, we…

We study, both analytically and numerically, the cascade of failures in two coupled network systems A and B, where multiple support-dependent relations are randomly built between nodes of networks A and B. In our model we assume that each…

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…

In complex networks the degrees of adjacent nodes may often appear dependent -- which presents a modelling challenge. We present a working framework for studying networks with an arbitrary joint distribution for the degrees of adjacent…

In many real, directed networks, the strongly connected component of nodes which are mutually reachable is very small. This does not fit with current theory, based on random graphs, according to which strong connectivity depends on mean…

It is known that the critical probability for the percolation transition is not a sharp threshold, actually it is a region of non-zero width $\Delta p_c$ for systems of finite size. Here we present evidence that for complex networks $\Delta…

A wireless communication network is considered where any two nodes are connected if the signal-to-interference ratio (SIR) between them is greater than a threshold. Assuming that the nodes of the wireless network are distributed as a…

Percolation theory characterizing the robustness of a network has applications ranging from biology, to epidemic spreading, and complex infrastructures. Percolation theory, however, only concern the typical response of a infinite network to…