Related papers: Deterministic Scale-Free Networks
We bring rigor to the vibrant activity of detecting power laws in empirical degree distributions in real-world networks. We first provide a rigorous definition of power-law distributions, equivalent to the definition of regularly varying…
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 propose a novel paradigm for modeling real-world scale-free networks, where the integration of new nodes is driven by the combined attractiveness of degree and betweenness centralities, the competition of which (expressed by a parameter…
There are many networks in real life which exist as form of Scale-free networks such as World Wide Web, protein-protein interaction network, semantic networks, airline networks, interbank payment networks, etc. If we want to analyze these…
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…
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…
We analyse growing networks ranging from collaboration graphs of scientists to the network of similarities defined among the various transcriptional profiles of living cells. For the explicit demonstration of the scale-free nature and…
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…
Generative mechanisms which lead to empirically observed structure of networked systems from diverse fields like biology, technology and social sciences form a very important part of study of complex networks. The structure of many…
We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…
We study ensemble-based graph-theoretical methods aiming to approximate the size of the minimum dominating set (MDS) in scale-free networks. We analyze both analytical upper bounds of dominating sets and numerical realizations for…
It is well-known that the scale-free networks are ubiquitous in nature and society and have been one of the hotspot topic in complex networks. Recently, scholars presented a large quantity of scale-free networks by calculating cumulative…
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…
We give an intuitive though general explanation of the finite-size effect in scale-free networks in terms of the degree distribution of the starting network. This result clarifies the relevance of the starting network in the final degree…
A variety of scale-free networks have been created since the pioneer work by A.-L. Barab\'{a}si and R. Albert. All this networks are homogeneous since they are composed of the same kind of nodes. In the realistic world, however, one element…
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…
We show that there are two classes of finite size effects for dynamic models taking place on a scale-free topology. Some models in finite networks show a behavior that depends only on the system size N. Others present an additional distinct…
Here we analyze the topology of the network formed by the minima and transition states on the potential energy landscape of small clusters. We find that this network has both a small-world and scale-free character. In contrast to other…
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…
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.…