Related papers: Optimal cost for strengthening or destroying a giv…
We study network configurations that provide optimal robustness to random breakdowns for networks with a given number of nodes $N$ and a given cost--which we take as the average number of connections per node $\kav$. We find that the…
The basic idea of many effective immunization strategies is first to rank the importance of vertices according to the degrees of vertices and then remove the vertices from highest importance to lowest until the network becomes disconnected.…
The scale-fee networks, having connectivity distribution $P(k)\sim k^{-\alpha}$ (where $k$ is the site connectivity), is very resilient to random failures but fragile to intentional attack. The purpose of this paper is to find the network…
We study numerically the cascading failure problem by using artificially created scale-free networks and the real network structure of the power grid. The capacity for a vertex is assigned as a monotonically increasing function of the load…
Network topology plays a key role in many phenomena, from the spreading of diseases to that of financial crises. Whenever the whole structure of a network is unknown, one must resort to reconstruction methods that identify the least biased…
Ranking the nodes' ability for spreading in networks is a fundamental problem which relates to many real applications such as information and disease control. In the previous literatures, a network decomposition procedure called k-shell…
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…
In the multidisciplinary field of Network Science, optimization of procedures for efficiently breaking complex networks is attracting much attention from practical points of view. In this contribution we present a module-based method to…
We introduce a collection of complex networks generated by a combination of preferential attachment and a previously unexamined process of "splitting" nodes of degree $k$ into $k$ nodes of degree 1. Four networks are considered, each…
Our goal is to quickly find top $k$ lists of nodes with the largest degrees in large complex networks. If the adjacency list of the network is known (not often the case in complex networks), a deterministic algorithm to find a node with the…
We study the fault-tolerance of networks from both the structural and computational point of view using the minimum leaf number of the corresponding graph $G$, i.e. the minimum number of leaves of the spanning trees of $G$, and its…
The process of destroying a complex network through node removal has been the subject of extensive interest and research. Node loss typically leaves the network disintegrated into many small and isolated clusters. Here we show that these…
We are interested in the design of robust (or resilient) capacitated rooted Steiner networks in case of terminals with uniform demands. Formally, we are given a graph, capacity and cost functions on the edges, a root, a subset of nodes…
In varying degree distributions, we investigate the optimally robust networks against targeted attacks to nodes with higher degrees. In considering that a network tends to have more robustness with a smaller variance of degree…
Much of our commerce and traveling depend on the efficient operation of large scale networks. Some of those, such as electric power grids, transportation systems, communication networks, and others, must maintain their efficiency even after…
We present a systematic and detailed study of the robustness of directed networks under random and targeted removal of links. We work with a set of network models of random and scale free type, generated with specific features of clustering…
It is a mainstream idea that scale-free network would be fragile under the selective attacks. Internet is a typical scale-free network in the real world, but it never collapses under the selective attacks of computer viruses and hackers.…
Complex networks have abundant and extensive applications in real life. Recently, researchers have proposed a number of complex networks, in which some are deterministic and others are random. Compared with deterministic networks, random…
Network robustness is a measure a network's ability to survive adversarial attacks. But not all parts of a network are equal. K-cores, which are dense subgraphs, are known to capture some of the key properties of many real-life networks.…
We consider optimal attacks or immunization schemes on different models of random graphs. We derive bounds for the minimum number of nodes needed to be removed from a network such that all remaining components are fragments of negligible…