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Influence of seed graph in preferential attachment model

We study the inuence of the seed graph in the preferential attachment model, focusing on the case of trees. We rst show that the seed has no eect from a weak local limit point of view. On the other hand, we conjecture that dierent seeds lead to dierent distributions of limiting trees from a total variation point of view.

We take a rst step in proving this conjecture by showing that seeds with dierent degree proles lead to dierent limiting distributions for the (appropriately normalized) maximum degree, implying that such seeds lead to dierent (in total variation) limiting trees

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