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We consider preferential attachment random graphs which may be obtained asfollows: It starts with a single node. If a new node appears, it is linked byan edge to one or more existing node(s) with a probability proportional tofunction of their degree. For a class of linear preferential attachment randomgraphs we find a large deviation principle (LDP) for the empirical degreemeasure. In the course of the prove this LDP we establish an LDP for theempirical degree and pair distribution see Theorem 2.3, of the fitnesspreferential attachment model of random graphs.

Large deviation principle for the empirical degree measure of preferential attachment random graphs