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We consider subgraph counts in general preferential attachment models withpower-law degree exponent $\tau>2$. For all subgraphs $H$, we find the scalingof the expected number of subgraphs as a power of the number of vertices. Weprove our results on the expected number of subgraphs by defining anoptimization problem that finds the optimal subgraph structure in terms of theindices of the vertices that together span it and by using the representationof the preferential attachment model as a P\'olya urn model.

Subgraphs in preferential attachment models