[4] R. Albert, H. Jeong, and A.-L. Barabási. Attack and error tolerance in

Efficiency of Scale-Free Networks: Error and Attack Tolerance

The concept of network efficiency, recently proposed to characterize the properties of small-world networks, is here used to study the effects of errors and attacks on scale-free networks. Two different kinds of scale-free networks, i.e. networks with power law P(k), are considered: 1) scale-free networks with no local clustering produced by the Barabasi-Albert model and 2) scale-free networks ...

The missing links in the BGP-based AS connectivity maps

A number of recent studies of the Internet topology at the autonomous systems level (AS graph) are based on the BGP-based AS connectivity maps (original maps). The so-called extended maps use additional data sources and contain more complete pictures of the AS graph. In this paper, we compare an original map, an extended map and a synthetic map generated by the Barabási-Albert model. We examine...

The Diameter of a Scale-Free Random Graph

We consider a random graph process in which vertices are added to the graph one at a time and joined to a fixed number m of earlier vertices, where each earlier vertex is chosen with probability proportional to its degree. This process was introduced by Barabási and Albert [3], as a simple model of the growth of real-world graphs such as the world-wide web. Computer experiments presented by Bar...

The Internet's Achilles' Heel: Error and attack tolerance of complex networks

The degree sequence of a scale-free random graph process

Recently, Barabási and Albert [2] suggested modeling complex real-world networks such as the worldwide web as follows: consider a random graph process in which vertices are added to the graph one at a time and joined to a fixed number of earlier vertices, selected with probabilities proportional to their degrees. In [2] and, with Jeong, in [3], Barabási and Albert suggested that after many step...