Related papers: Degree-Ordered-Percolation on uncorrelated network…
This paper presents a tighter bound on the degree distribution of arbitrary P\'{o}lya urn graph processes, proving that the proportion of vertices with degree $d$ obeys a power-law distribution $P(d) \propto d^{-\gamma}$ for $d \leq…
We study living neural networks by measuring the neurons' response to a global electrical stimulation. Neural connectivity is lowered by reducing the synaptic strength, chemically blocking neurotransmitter receptors. We use a…
We investigate choice-driven network growth. In this model, nodes are added one by one according to the following procedure: for each addition event a set of target nodes is selected, each according to linear preferential attachment, and a…
In the modeling, monitoring, and control of complex networks, a fundamental problem concerns the comprehensive determination of the state of the system from limited measurements. Using power grids as example networks, we show that this…
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…
In this work we explore degree assortativity in complex networks, and extend its usual definition beyond that of nearest neighbours. We apply this definition to model networks, and describe a rewiring algorithm that induces assortativity.…
We introduce a scalable searching algorithm for finding nodes and contents in random networks with Power-Law (PL) and heavy-tailed degree distributions. The network is searched using a probabilistic broadcast algorithm, where a query…
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…
We describe the anomalous phase transition of the emergence of the giant connected component in scale-free networks growing under mechanism of preferential linking. We obtain exact results for the size of the giant connected component and…
It is known that the critical probability for the percolation transition is not a sharp threshold, actually it is a region of non-zero width $\Delta p_c$ for systems of finite size. Here we present evidence that for complex networks $\Delta…
We obtain closed form expressions for the expected conditional degree distribution and the joint degree distribution of the linear preferential attachment model for network growth in the steady state. We consider the multiple-destination…
Recently it has been demonstrated that the connectivity transition from microscopic connectivity to macroscopic connectedness, known as percolation, is generically announced by a cascade of microtransitions of the percolation order…
We consider robustness and percolation properties of the networks of networks, in which random nodes in different individual networks (layers) can be interdependent. We explore the emergence of the giant mutually connected component,…
We propose the $K$-selective percolation process as a model for the iterative removals of nodes with the specific intermediate degree in complex networks. In the model, a random node with degree $K$ is deactivated one by one until no more…
We study delay tolerant networking (DTN) and in particular, its capacity to store, carry and forward messages so that the messages eventually reach their final destinations. We approach this broad question in the framework of percolation…
It has been recently shown that the percolation transition is discontinuous in Erd\H{o}s-R\'enyi networks and square lattices in two dimensions under the Achlioptas Process (AP). Here, we show that when the structure is highly heterogeneous…
We investigate bond percolation on mediation-driven attachment (MDA) networks under the generalized Achlioptas process, where $M>1$ candidate bonds are sampled and the one that minimizes the resulting cluster size is selected the…
Scale-free networks with small power law exponent are known to be robust, meaning that their qualitative topological structure cannot be altered by random removal of even a large proportion of nodes. By contrast, it has been argued in the…
Percolation in complex networks is viewed as both: a process that mimics network degradation and a tool that reveals peculiarities of the underlying network structure. During the course of percolation, networks undergo non-trivial…
The shortest-path percolation (SPP) model aims at describing the consumption and eventual exhaustion of a network's resources. Starting from a network containing a macroscopic connected component, random pairs of nodes are sequentially…