A random graph model for power law graphs

We propose a random graph model which is a special case of sparse random gr aphs with given degree sequences which satisfy a power law. This model invo lves only a small number of parameters, called logsize and log-log growth r ate. These parameters capture some universal characteristics of massive gra phs. From these parameters, various properties of the graph can be derived. For example, for certain ranges of the parameters, we will compute the exp ected distribution of the sizes of the connected components which almost su rely occur with high probability. We illustrate the consistency of our mode l with the behavior of some massive graphs derived from data in telecommuni cations. We also discuss the threshold function, the giant component, and t he evolution of random graphs in this model.