Abstract:
We study a model of a random graph of the type of the
Barabási–Albert preferential attachment model.
We develop a technique that makes it possible
to estimate the mathematical expectation for a fairly wide
class of random variables in the model under consideration.
We use this technique to prove
a theorem on the asymptotics of the mathematical expectation
of the number of subgraphs isomorphic to a certain fixed graph
in the random graphs of this model.
Keywords:random graph, Internet graph, preferential attachment,
Barabási–Albert model, number of subgraphs.
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