相关论文: Percolation in networks composed of connectivity a…
We study the large-deviation properties of minimum spanning trees for two ensembles of random graphs with $N$ nodes. First, we consider complete graphs. Second, we study Erd\H{o}s-R\'{e}nyi (ER) random graphs with edge probability $p=c/N$…
We study the cascading failure of networks due to overload, using the betweenness centrality of a node as the measure of its load following the Motter and Lai model. We study the fraction of survived nodes at the end of the cascade $p_f$ as…
Systems which consist of many localized constituents interacting with each other can be represented by complex networks. Consistently, network science has become highly popular in vast fields focusing on natural, artificial and social…
Many systems such as critical infrastructure exhibit a modular structure with many links within the modules and few links between them. One approach to increase the robustness of these systems is to reinforce a fraction of the nodes in each…
We introduce the concept of boundaries of a complex network as the set of nodes at distance larger than the mean distance from a given node in the network. We study the statistical properties of the boundaries nodes of complex networks. We…
We use the configuration model to generate networks having a degree distribution that follows a $q$-exponential, $P_q(k)=(2-q)\lambda[1-(1-q)\lambda k]^{1/(q-1)}$, for arbitrary values of the parameters $q$ and $\lambda$. We study the…
The diffusion and bootstrap percolation models were studied in regular random and Erd\H{o}s-R\'{e}nyi networks using the modified Newman-Ziff algorithms. We calculated the percolation threshold and the order parameter of the percolation…
The micro-structure of the giant component of the Erd{\H o}s-R\'enyi network and other configuration model networks is analyzed using generating function methods. While configuration model networks are uncorrelated, the giant component…
We apply percolation theory to a recently proposed measure of fragmentation $F$ for social networks. The measure $F$ is defined as the ratio between the number of pairs of nodes that are not connected in the fragmented network after…
Many networks are characterized by highly heterogeneous distributions of links, which are called scale-free networks and the degree distributions follow $p(k)\sim ck^{-\alpha}$. We study the robustness of scale-free networks to random…
A common theme among the proposed models for network epidemics is the assumption that the propagating object, i.e., a virus or a piece of information, is transferred across the nodes without going through any modification or evolution.…
A bredge (bridge-edge) is an edge whose deletion would split the network component on which it resides into two components. Bredges are vulnerable links that play an important role in network collapse processes, which may result from node…
In the last two decades, network science has blossomed and influenced various fields, such as statistical physics, computer science, biology and sociology, from the perspective of the heterogeneous interaction patterns of components…
Practical wireless networks are finite, and hence non-stationary with nodes typically non-homo-geneously deployed over the area. This leads to a location-dependent performance and to boundary effects which are both often neglected in…
Looking to overcome the limitations of traditional networks, the network science community has lately given much attention to the so-called higher-order networks, where group interactions are modeled alongside pairwise ones. While degree…
We examine the heterogeneous responses of individual nodes in sparse networks to the random removal of a fraction of edges. Using the message-passing formulation of percolation, we discover considerable variation across the network in the…
In many cases of attacks or failures, memory effects play a significant role. Therefore, we present a model that not only considers the dependencies between nodes but also incorporates the memory effects of attacks. Our research…
In a recent Letter, Friedman and Landsberg discussed the underlying mechanism of explosive phase transitions on complex networks [Phys. Rev. Lett. 103, 255701 (2009)]. This Brief Report presents a modest, though more insightful extension of…
Degree correlation is an important topological property common to many real-world networks. In this paper, the statistical measures for characterizing the degree correlation in networks are investigated analytically. We give an exact proof…
The Erdos-Renyi classical random graph is characterized by a fixed linking probability for all pairs of vertices. Here, this concept is generalized by drawing the linking probability from a certain distribution. Such a procedure is found to…