Related papers: Two complementary representations of a scale-free …

We introduce a deterministic model for scale-free networks, whose degree distribution follows a power-law with the exponent $\gamma$. At each time step, each vertex generates its offsprings, whose number is proportional to the degree of…

A scale-free network is grown in the Euclidean space with a global directional bias. On a vertical plane, nodes are introduced at unit rate at randomly selected points and a node is allowed to be connected only to the subset of nodes which…

This article addresses the degree distribution of subnetworks, namely the number of links between the nodes in each subnetwork and the remainder of the structure (cond-mat/0408076). The transformation from a subnetwork-partitioned model to…

We introduce a new family of models for growing networks. In these networks new edges are attached preferentially to vertices with higher number of connections, and new vertices are created by already existing ones, inheriting part of their…

We propose a simple dynamical model that generates networks with power-law degree distributions with the exponent 2 through rewiring only. At each time step, two nodes, i and j, are randomly selected, and one incoming link to i is…

We define gradient networks as directed graphs formed by local gradients of a scalar field distributed on the nodes of a substrate network G. We derive an exact expression for the in-degree distribution of the gradient network when the…

Based on the empirical analysis of the dependency network in 18 Java projects, we develop a novel model of network growth which considers both: an attachment mechanism and the addition of new nodes with a heterogeneous distribution of their…

We use the configuration model to generate networks having a degree distribution that follows a $q$-exponential, $P_q(k)=(2-q)\lambda[1-(1-q)\lambda k]^{1/(q-1)}$, for arbitrary values of the parameters $q$ and $\lambda$. We study the…

There is increasing evidence that dense networks occur in on-line social networks, recommendation networks and in the brain. In addition to being dense, these networks are often also scale-free, i.e. their degree distributions follow…

We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes…

Here, we propose a class of scale-free networks $G(t;m)$ with some intriguing properties, which can not be simultaneously held by all the theoretical models with power-law degree distribution in the existing literature, including (i)…

Generally, the threshold of percolation in complex networks depends on the underlying structural characterization. However, what topological property plays a predominant role is still unknown, despite the speculation of some authors that…

Scale-free networks, in which the distribution of the degrees obeys a power-law, are ubiquitous in the study of complex systems. One basic network property that relates to the structure of the links found is the degree assortativity, which…

We propose a possible relation between complex networks and gravity. Our guide in our proposal is the power-law distribution of the node degree in network theory and the information approach to gravity. The established bridge may allow us…

Complex networks have been studied extensively due to their relevance to many real systems as diverse as the World-Wide-Web (WWW), the Internet, energy landscapes, biological and social networks…

It has been claimed that protein-protein interaction (PPI) networks are scale-free based on the observation that the node degree sequence follows a power law. Here we argue that these claims are likely to be based on erroneous statistical…

The scale free structure p(k)~k^{-gamma} of protein-protein interaction networks can be reproduced by a static physical model in simulation. We inspect the model theoretically, and find the key reason for the model to generate apparent…

Approaches from statistical physics are applied to investigate the structure of network models whose growth rules mimic aspects of the evolution of the world-wide web. We first determine the degree distribution of a growing network in which…

Unlike the well-studied models of growing networks, where the dominant dynamics consist of insertions of new nodes and connections, and rewiring of existing links, we study {\em ad hoc} networks, where one also has to contend with rapid and…

What is the underlying mechanism leading to power-law degree distributions of many natural and artificial networks is still at issue. We consider that scale-free networks emerges from self-organizing process, and such a evolving model is…