# On the influence of the seed graph in the preferential attachment model

arXiv: https://arxiv.org/abs/1401.4849 · HTML: https://mlsanity.com/paper/1401.4849/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jan 2014.

## Built on by (most cited first, 2 of 2)

- [Archaeology of random recursive dags and Cooper-Frieze random networks](https://mlsanity.com/paper/2207.14601/) (2022)
- [Harnessing Multiple Correlated Networks for Exact Community Recovery](https://mlsanity.com/paper/2412.02796/) (2024)

## Abstract (arXiv)

We study the influence of the seed graph in the preferential attachment model, focusing on the case of trees. We first show that the seed has no effect from a weak local limit point of view. On the other hand, we conjecture that different seeds lead to different distributions of limiting trees from a total variation point of view. We take a first step in proving this conjecture by showing that seeds with different degree profiles lead to different limiting distributions for the (appropriately normalized) maximum degree, implying that such seeds lead to different (in total variation) limiting trees.