Related papers: Criticality in Random Threshold Networks: Annealed…
We develop a phenomenological theory of critical phenomena in networks with an arbitrary distribution of connections $P(k)$. The theory shows that the critical behavior depends in a crucial way on the form of $P(k)$ and differs strongly…
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…
Percolation is a fundamental concept that brought new understanding on the robustness properties of complex systems. Here we consider percolation on weakly interacting networks, that is, network layers coupled together by much less…
We study the detailed mechanism of the failure of scale-free networks under intentional attacks. Although it is generally accepted that such networks are very sensitive to targeted attacks, we show that for a particular type of structure…
Using probabilistic approach, the transient dynamics of sparsely connected Hopfield neural networks is studied for arbitrary degree distributions. A recursive scheme is developed to determine the time evolution of overlap parameters. As…
We introduce and study systems of randomly coupled maps (RCM) where the relevant parameter is the degree of connectivity in the system. Global (almost-) synchronized states are found (equivalent to the synchronization observed in globally…
Recently it was shown (I.A.Gruzberg, A. Kl\"umper, W. Nuding and A. Sedrakyan, Phys.Rev.B 95, 125414 (2017)) that taking into account random positions of scattering nodes in the network model with $U(1)$ phase disorder yields a localization…
We present an algorithm for generating random networks with arbitrary degree distribution and Clustering (frequency of triadic closure). We use this algorithm to generate networks with exponential, power law, and poisson degree…
We analyze critical phenomena on networks generated as the union of hidden variables models (networks with any desired degree sequence) with arbitrary graphs. The resulting networks are general small-worlds similar to those a` la Watts and…
We study the effect of assortative and disassortative mixing on the robustness of networks under random node failures. For ordinary (dyadic) networks, by using the generating function technique and stochastic simulations, we show that the…
Large cascades are a common occurrence in many natural and engineered complex systems. In this paper we explore the propagation of cascades across networks using realistic network topologies, such as heterogeneous degree distributions, as…
We present the mathematical analysis of generalized complex contagions in clustered multiplex networks for susceptible-infected-recovered (SIR)-like dynamics. The model is intended to understand diffusion of influence, or any other…
We investigate certain structural properties of random interdependent networks. We start by studying a property known as $r$-robustness, which is a strong indicator of the ability of a network to tolerate structural perturbations and…
Motivated by the analysis of social networks, we study a model of random networks that has both a given degree distribution and a tunable clustering coefficient. We consider two types of growth processes on these graphs: diffusion and…
We discuss how various models of scale-free complex networks approach their limiting properties when the size N of the network grows. We focus mainly on equilibrated networks and their finite-size degree distributions. Our results show that…
We introduce a model for dynamic networks, where the links or the strengths of the links change over time. We solve the model by mapping dynamic networks to the problem of directed percolation, where the direction corresponds to the…
The formation of sintering bridges in amorphous powders affects both flow behavior and perceived material quality. When sintering is driven by surface tension, bridges emerge sequentially, favoring contacts between smaller particles first.…
We study a spatial network model with exponentially distributed link-lengths on an underlying grid of points, undergoing a structural crossover from a random, Erd\H{o}s--R\'enyi graph to a $2D$ lattice at the characteristic interaction…
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…
We study the simple random walk dynamics on an annealed version of a Small-World Network (SWN) consisting of $N$ nodes. This is done by calculating the mean number of distinct sites visited S(n) and the return probability $P_{00}(t)$ as a…