Related papers: Are Scale Free Networks Better?
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…
A growing family of random graphs is called robust if it retains a giant component after percolation with arbitrary positive retention probability. We study robustness for graphs, in which new vertices are given a spatial position on the…
Getting good statistical models of traffic on network links is a well-known, often-studied problem. A lot of attention has been given to correlation patterns and flow duration. The distribution of the amount of traffic per unit time is an…
Probabilistic networks display a wide range of high average clustering coefficients independent of the number of nodes in the network. In particular, the local clustering coefficient decreases with the degree of the subtending node in a…
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…
How does the shape of a network change as its size increases? Although random graph models provide some expectations for such "scaling behaviors" in the structure of networks, relatively little is known about how empirical network structure…
Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This…
We investigate the statistics of the most connected nodes in scale-free networks. For a scale-free network model with homogeneous nodes, we show by means of extensive simulations that the exponential truncation--due to the finite size of…
Getting good statistical models of traffic on network links is a well-known, often-studied problem. A lot of attention has been given to correlation patterns and flow duration. The distribution of the amount of traffic per unit time is an…
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…
In this paper, we present a simple model of scale-free networks that incorporates both preferential & random attachment and anti-preferential & random deletion at each time step. We derive the degree distribution analytically and show that…
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…
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…
In this paper we theoretically and empirically study the degree and connectivity of the Internet's scale-free topology at the autonomous system (AS) level. The basic features of the scale-free network have influence on the normalization…
Many real-world scale-free networks, such as neural networks and online communication networks, consist of a fixed number of nodes but exhibit dynamic edge fluctuations. However, traditional models frequently overlook scenarios where the…
The topology of an instant messaging system is described. Statistical measures of the network are given and compared with the statistics of a comparable random graph. The scale-free character of the network is examined and implications are…
The increased availability of data on real networks has favoured an explosion of activity in the elaboration of models able to reproduce both qualitatively and quantitatively the measured properties. What has been less explored is the…
A central claim in modern network science is that real-world networks are typically "scale free," meaning that the fraction of nodes with degree $k$ follows a power law, decaying like $k^{-\alpha}$, often with $2 < \alpha < 3$. However,…
We show how scale-free degree distributions can emerge naturally from growing networks by using random walks for selecting vertices for attachment. This result holds for several variants of the walk algorithm and for a wide range of…
In this paper, we compare the number of unmatched nodes and the size of dilations in two main random network models, the Scale-Free and Clustered Scale-Free networks. The number of unmatched nodes determines the necessary number of control…