Related papers: Network robustness and fragility: Percolation on r…

Graphs are pervasive in our everyday lives, with relevance to biology, the internet, and infrastructure, as well as numerous other applications. It is thus necessary to have an understanding as to how quickly a graph disintegrates, whether…

We develop a new ensemble of modular random graphs in which degree-degree correlations can be different in each module and the inter-module connections are defined by the joint degree-degree distribution of nodes for each pair of modules.…

We introduce models of generic rigidity percolation in two dimensions on hierarchical networks, and solve them exactly by means of a renormalization transformation. We then study how the possibility for the network to self organize in order…

Many real-world networks display a community structure. We study two random graph models that create a network with similar community structure as a given network. One model preserves the exact community structure of the original network,…

In real networks, the dependency between nodes is ubiquitous; however, the dependency is not always complete and homogeneous. In this paper, we propose a percolation model with weak and heterogeneous dependency; i.e., dependency strengths…

Percolation is perhaps the simplest example of a process exhibiting a phase transition and one of the most studied phenomena in statistical physics. The percolation transition is continuous if sites/bonds are occupied independently with the…

Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…

In wireless networks, the knowledge of nodal distances is essential for several areas such as system configuration, performance analysis and protocol design. In order to evaluate distance distributions in random networks, the underlying…

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…

The importance of studying properties of networks is manifest in diverse fields ranging from biology, engineering, physics, chemistry, neuroscience, and medicine. The functionality of networks with regard to performance, throughput,…

Infrastructure systems, such as power, transportation, telecommunication, and water systems, are composed of multiple components which are interconnected and interdependent to produce and distribute essential goods and services. So, the…

One of the most influential recent results in network analysis is that many natural networks exhibit a power-law or log-normal degree distribution. This has inspired numerous generative models that match this property. However, more recent…

Random intersection graphs have received much attention for nearly two decades, and currently have a wide range of applications ranging from key predistribution in wireless sensor networks to modeling social networks. In this paper, we…

In a recent work [Proc. Natl. Acad. Sci. USA 108, 3838 (2011)], Schneider et al. proposed a new measure for network robustness and investigated optimal networks with respect to this quantity. For networks with a power-law degree…

We investigate the following vertex percolation process. Starting with a random regular graph of constant degree, delete each vertex independently with probability p, where p=n^{-alpha} and alpha=alpha(n) is bounded away from 0. We show…

We consider different methods, that do not rely on numerical simulations of the percolation process, to approximate percolation thresholds in networks. We perform a systematic analysis on synthetic graphs and a collection of 109 real…

Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…

We study tolerance and topology of random scale-free networks under attack and defense strategies that depend on the degree k of the nodes. This situation occurs, for example, when the robustness of a node depends on its degree or in an…

We investigate spatial random graphs defined on the points of a Poisson process in $d$-dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point is assigned an independent weight. Given the…

Complex networks have been applied to model numerous interactive nonlinear systems in the real world. Knowledge about network topology is crucial for understanding the function, performance and evolution of complex systems. In the last few…