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.