Scientific publications

We consider configuration graphs with N vertices under the condition that the sum of vertex degrees is bounded from above by n. The degrees of vertices are independed and identically distributed according to an unknown distribution law which depends on a slowly varying function and has finite expectation and variance. Such models can be used to describe various communication networks and Internet topology. The paper finds the limit distributions of the maximum vertex degree and the number of vertices with a given degree as N,n→∞.