Related papers: Scale-free network on a vertical plane
Through the distinction between ``real'' and ``virtual'' links between the nodes of a graph, we develop a set of simple rules leading to scale-free networks with a tunable degree distribution exponent. Albeit sharing some similarities with…
We offer an example of an network model with a power law degree distribution, P(k) ~ k^{-alpha}, for nodes but which nevertheless has a well-defined geography and a nonzero threshold percolation probability for alpha>2, the range of…
We consider a growing network, whose growth algorithm is based on the preferential attachment typical for scale-free constructions, but where the long-range bonds are disadvantaged. Thus, the probability to get connected to a site at…
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…
Scaling behavior of scale-free evolving networks arising in communications, citations, collaborations, etc. areas is studied. We derive universal scaling relations describing properties of such networks and indicate limits of their…
We study Erd\"{o}s-R\'enyi random graphs with random weights associated with each link. We generate a new ``Supernode network'' by merging all nodes connected by links having weights below the percolation threshold (percolation clusters)…
Recently there have been a tremendous interest in models of networks with a power-law distribution of degree -- so called "scale-free networks." It has been observed that such networks, normally, have extremely short path-lengths, scaling…
We suggest a method for embedding scale-free networks, with degree distribution P(k) k^-lambda, in regular Euclidean lattices. The embedding is driven by a natural constraint of minimization of the total length of the links in the system.…
Using a simple model with link removals as well as link additions, we show that an evolving network is scale free with a degree exponent in the range of (2, 4]. We then establish a relation between the network evolution and a set of…
The rate equations are used to study the scale-free behavior of the weight distribution in evolving networks whose topology is determined only by degrees of preexisting vertices. An analysis of these equations shows that the degree…
We study scale free simple graphs with an exponent of the degree distribution $\gamma$ less than two. Generically one expects such extremely skewed networks -- which occur very frequently in systems of virtually or logically connected units…
We introduce a simple one-parameter network growth algorithm which is able to reproduce a wide variety of realistic network structures but without having to invoke any global information about node degrees such as preferential-attachment…
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 study the diameter, or the mean distance between sites, in a scale-free network, having N sites and degree distribution p(k) ~ k^-a, i.e. the probability of having k links outgoing from a site. In contrast to the diameter of regular…
Many complex systems--from social and communication networks to biological networks and the Internet--are thought to exhibit scale-free structure. However, prevailing explanations rely on the constant addition of new nodes, an assumption…
We generalize the degree-organizational view of real-world networks with broad degree-distributions in a landscape analogue with mountains (high-degree nodes) and valleys (low-degree nodes). For example, correlated degrees between adjacent…
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.…
We investigate a network model based on an infinite regular square lattice embedded in the Euclidean plane where the node connection probability is given by the geometrical distance of nodes. We show that the degree distribution in the…
We present a novel type of weighted scale-free network model, in which the weight grows independently of the attachment of new nodes. The evolution of this network is thus determined not only by the preferential attachment of new nodes to…
The impact of inhomogeneous arrangement of nodes in space on network organization cannot be neglected in most of real-world scale-free networks. Here, we wish to suggest a model for a geographical network with nodes embedded in a fractal…