Geodesic
On the number of subgraphs of the Barab\'asi--Albert random graph
Izvestiya. Mathematics , Tome 76 (2012) no. 3, pp. 607-625

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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, preferential attachment, Barabási–Albert model, number of subgraphs.
Mots-clés : Internet graph 
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     author = {A. A. Ryabchenko and E. A. Samosvat},
     title = {On the number of subgraphs of the {Barab\'asi--Albert} random graph},
     journal = {Izvestiya. Mathematics },
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     publisher = {mathdoc},
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     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2012_76_3_a7/}
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A. A. Ryabchenko; E. A. Samosvat. On the number of subgraphs of the Barab\'asi--Albert random graph. Izvestiya. Mathematics , Tome 76 (2012) no. 3, pp. 607-625. http://geodesic.mathdoc.fr/item/IM2_2012_76_3_a7/