Related papers: All scale-free networks are sparse
We propose a model for growing networks based on a finite memory of the nodes. The model shows stylized features of real-world networks: power law distribution of degree, linear preferential attachment of new links and a negative…
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…
Many realistic networks are scale-free, with small characteristic path lengths, high clustering, and power law in their degree distribution. They can be obtained by dynamical networks in which a preferential attachment process takes place.…
We provide a simple proof that graphs in a general class of self-similar networks have zero percolation threshold. The considered self-similar networks include random scale-free graphs with given expected node degrees and zero clustering,…
Complex networks are characterized by several topological properties: degree distribution, clustering coefficient, average shortest path length, etc. Using a simple model to generate scale-free networks embedded on geographical space, we…
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…
In this paper, a simply rule that generates scale-free networks with very large clustering coefficient and very small average distance is presented. These networks are called {\bf Multistage Random Growing Networks}(MRGN) as the adding…
In this paper we model the tomography of scale free networks by studying the structure of layers around an arbitrary network node. We find, both analytically and empirically, that the distance distribution of all nodes from a specific…
Scale-free power law structure describes complex networks derived from a wide range of real world processes. The extensive literature focuses almost exclusively on networks with power law exponent strictly larger than 2, which can be…
Empirical evidence suggests that heavy-tailed degree distributions occurring in many real networks are well-approximated by power laws with exponents $\eta$ that may take values either less than and greater than two. Models based on various…
Networks with a scale-free degree distribution are widely thought to promote cooperation in various games. Herein, by studying the well-known prisoner's dilemma game, we demonstrate that this need not necessarily be true. For the very same…
A random network is grown by introducing at unit rate randomly selected nodes on the Euclidean space. A node is randomly connected to its $i$-th predecessor of degree $k_i$ with a directed link of length $\ell$ using a probability…
A projective network model is a model that enables predictions to be made based on a subsample of the network data, with the predictions remaining unchanged if a larger sample is taken into consideration. An exchangeable model is a model…
Scale-free networks are abundant in nature and society, describing such diverse systems as the world wide web, the web of human sexual contacts, or the chemical network of a cell. All models used to generate a scale-free topology are…
We propose a geometric growth model for weighted scale-free networks, which is controlled by two tunable parameters. We derive exactly the main characteristics of the networks, which are partially determined by the parameters. Analytical…
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 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…
There is a pressing need for a description of complex systems that includes considerations of the underlying network of interactions, for a diverse range of biological, technological and other networks. In this work relationships between…
Learning the network structure underlying data is an important problem in machine learning. This paper introduces a novel prior to study the inference of scale-free networks, which are widely used to model social and biological networks.…
In many networks such as transportation or communication networks, distance is certainly a relevant parameter. In addition, real-world examples suggest that when long-range links are existing, they usually connect to hubs-the well connected…