, for a very general class of underlying degree distributions, explicitly calculate the distribution that will be observed. As example applications of our machinery, we prove that traceroute sampling finds power-law degree distributions in both δ-regular and Poisson-distributed random graphs. Thus, our

and PageRank distributionsof these complex networks conform to the Power-Law distribution. This paper utilizes the degree distribution of a network to initialize its PageRank vector, and presents a Power-Law degree distribution accelerating algorithm of PageRank computation. Experiments on four real

those other nodes already have. Power-law degree distributions, however, may also well describe degree distributions that result when averaging across multiple individual degree distributions, none of which follows a power-law. Further, each of these individual distributions may reflect a random growth

We will examine models of graphs that exhibit degree distributions that satisfy power laws. These are inspired by the models in [BA99, KRR + 00]. We will see: 1. Simulations results. 2. The method of heuristic analysis from [BA99]. 3. A heuristic treatment, from [Mit03], of the analysis of [KRR

on related to complex networks: Small worlds: Even though the complex networks are often large, in most networks there is a relatively short path between any two nodes. One of the most popular manifestations of small worlds is the “six degrees of separation ” which concludes that, in a social network

It is shown that in a subcritical random graph with given vertex degrees satisfying a power law degree distribution with exponent γ>3, the largest component is of order n 1/(γ −1). More precisely, the order of the largest component is approximatively given by a simple constant times the largest

traceroute sampling finds power-law degree distributions in both δ-regular and Poisson-distributed random graphs. Thus, our work puts the observations of Lakhina et al. on a rigorous footing, and extends them to nearly arbitrary degree distributions.

If we consider the contact process with infection rate λ on a random graph on n vertices with power law degree distributions, mean field calculations suggest that the critical value λc of the infection rate is positive if the power α> 3. Physicists seem to regard this as an established fact

{alessandra, htzheng, ravenben}

tunable power-law degree distribution and