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The vulnerability of networks to targeted attacks is an issue of widespread interest for policymakers, military strategists, network engineers and systems biologists alike. Current approaches to circumvent targeted attacks seek to increase…
In this paper, site percolation on random $\Phi^{3}$ planar graphs is studied by Monte-Carlo numerical techniques. The method consists in randomly removing a fraction $q=1-p$ of vertices from graphs generated by Monte-Carlo simulations,…
There has been a considerable amount of interest in recent years on the robustness of networks to failures. Many previous studies have concentrated on the effects of node and edge removals on the connectivity structure of a static network;…
We propose and analyze a stochastic model which explains, analytically, the cutoff behavior of real scale-free networks previously modeled computationally by Amaral et al. [Proc. Natl. Acad. Sci. U.S.A. 97, 11149 (2000)] and others. We…
There have been several spectral bounds for the percolation transition in networks, using spectrum of matrices associated with the network such as the adjacency matrix and the non-backtracking matrix. However they are far from being tight…
We introduce a random bit-string model of post-transcriptional genetic regulation based on sequence matching. The model spontaneously yields a scale free network with power law scaling with $ \gamma=-1$ and also exhibits log-periodic…
Using an inverse of the standard linear congruential random number generator, large randomly occupied lattices can be visited by a random walker without having to determine the occupation status of every lattice site in advance. In seven…
We study some simple models of disease transmission on small-world networks, in which either the probability of infection by a disease or the probability of its transmission is varied, or both. The resulting models display epidemic behavior…
Many man-made networks support each other to provide efficient services and resources to the customers, despite that this support produces a strong interdependency between the individual networks. Thus an initial failure of a fraction $1-p$…
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 investigate the spread of diseases, computer viruses or information on complex networks and also immunization strategies to prevent or control the spread. When an entire population cannot be immunized and the effect of immunization is…
We propose a general model of unweighted and undirected networks having the scale-free property and fractal nature. Unlike the existing models of fractal scale-free networks (FSFNs), the present model can systematically and widely change…
In this paper, we analyze the nature and distribution of structured data on the Web. Web-scale information extraction, or the problem of creating structured tables using extraction from the entire web, is gathering lots of research…
In the present article, numerical simulations have been performed to find the bond and site percolation thresholds on two-dimensional Gabriel graphs (GG) for Poisson point processes. GGs belong to the family of proximity graphs and are…
We study the response of complex networks subject to attacks on vertices and edges. Several existing complex network models as well as real-world networks of scientific collaborations and Internet traffic are numerically investigated, and…
Critical phenomena on scale-free networks with a degree distribution $p_k \sim k^{-\lambda}$ exhibit rich finite-size effects due to its structural heterogeneity. We systematically study the finite-size scaling of percolation and identify…
In this Letter, we show that the explosive percolation is a novel continuous phase transition. The order-parameter-distribution histogram at the percolation threshold is studied in Erd\H{o}s-R\'{e}nyi networks, scale-free networks, and…
In this paper we study the small-world network model of Watts and Strogatz, which mimics some aspects of the structure of networks of social interactions. We argue that there is one non-trivial length-scale in the model, analogous to the…
The percolation threshold of the network model by Barabasi and Albert (BA-model) [Science 286, 509 (1999)] has thus far only been 'guessed' based on simulations and comparison with other models. Due to the still uncertain influence of…
It is commonly believed that scale-free networks are robust to massive numbers of random node deletions. For example, Cohen et al. study scale-free networks including some which approximate the measured degree distribution of the Internet.…