Related papers: Vulnerability of robust preferential attachment ne…

The classical preferential attachment model is sensitive to the choice of the initial configuration of the network. As the number of initial nodes and their degree grow, so does the time needed for an equilibrium degree distribution to be…

Inspired by empirical data on real world complex networks, the last few years have seen an explosion in proposed generative models to understand and explain observed properties of real world networks, including power law degree distribution…

From the proliferative mechanisms generating neurons from progenitor cells to neuron migration and synaptic connection formation, several vicissitudes culminate in the mature brain. Both component loss and gain remain ubiquitous during…

We study the robustness of complex networks subject to edge removal. Several network models and removing strategies are simulated. Rather than the existence of the giant component, we use total connectedness as the criterion of breakdown.…

Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This…

We show that in preferential attachment models with power-law exponent $\tau\in(2,3)$ the distance between randomly chosen vertices in the giant component is asymptotically equal to $(4+o(1))\, \frac{\log\log N}{-\log (\tau-2)}$, where $N$…

We propose a scale-free network model with a tunable power-law exponent. The Poisson growth model, as we call it, is an offshoot of the celebrated model of Barab\'{a}si and Albert where a network is generated iteratively from a small seed…

We study the contact process on a class of evolving scale-free networks, where each node updates its connections at independent random times. We give a rigorous mathematical proof that there is a transition between a phase where for all…

Biased (degree-dependent) percolation was recently shown to provide new strategies for turning robust networks fragile and vice versa. Here we present more detailed results for biased edge percolation on scale-free networks. We assume a…

We propose a model that generates a new class of networks exhibiting power-law degree distribution with a spectrum of exponents depending on the number of links ($m$) with which incoming nodes join the existing network. Unlike the…

The behavior of complex networks under attack depends strongly on the specific attack scenario. Of special interest are scale-free networks, which are usually seen as robust under random failure or attack but appear to be especially…

The behaviour of complex networks under failure or attack depends strongly on the specific scenario. Of special interest are scale-free networks, which are usually seen as robust under random failure but appear to be especially vulnerable…

Extensive studies have been done to understand the principles behind architectures of real networks. Recently, evidences for hierarchical organization in many real networks have also been reported. Here, we present a new hierarchical model…

A majority of studied models for scale-free networks have degree distributions with exponents greater than $2$. Real networks, however, can demonstrate essentially more heavy-tailed degree distributions. We explore two models of scale-free…

We developed a scheme for evaluating the size of the largest connected subnetwork (giant component) in random networks and the percolation threshold when sites (nodes) and/or bonds (edges) are removed from the networks based on the cavity…

Robust control theory has been successfully applied to numerous real-world problems using a small set of devices called {\it controllers}. However, the real systems represented by networks contain unreliable components and modern robust…

If we add links to a network at random, a critical threshold can be crossed where a giant connected component forms. Conversely, if links or nodes are removed at random, the giant component shrinks and eventually breaks. In this paper, we…

A network growth mechanism based on a two-step preferential rule is investigated as a model of network growth in which no global knowledge of the network is required. In the first filtering step a subset of fixed size $m$ of existing nodes…

A two state sandpile model with preferential sand distribution is developed and studied numerically on scale free networks with power-law degree ($k$) distribution, {\em i.e.}: $P_k\sim k^{-\alpha}$. In this model, upon toppling of a…

There has been considerable recent interest in the properties of networks, such as citation networks and the worldwide web, that grow by the addition of vertices, and a number of simple solvable models of network growth have been studied.…