# Analysis of centrality in sublinear preferential attachment trees via the CMJ branching process

arXiv: https://arxiv.org/abs/1601.06448 · HTML: https://mlsanity.com/paper/1601.06448/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jan 2016.

## Built on by (most cited first, 3 of 3)

- [Archaeology of random recursive dags and Cooper-Frieze random networks](https://mlsanity.com/paper/2207.14601/) (2022)
- [Estimating the history of a random recursive tree](https://mlsanity.com/paper/2403.09755/) (2024)
- [Leaf Stripping on Uniform Attachment Trees](https://mlsanity.com/paper/2410.06481/) (2024)

## Abstract (arXiv)

We investigate centrality and root-inference properties in a class of growing random graphs known as sublinear preferential attachment trees. We show that a continuous time branching processes called the Crump-Mode-Jagers (CMJ) branching process is well-suited to analyze such random trees, and prove that almost surely, a unique terminal tree centroid emerges, having the property that it becomes more central than any other fixed vertex in the limit of the random growth process. Our result generalizes and extends previous work establishing persistent centrality in uniform and linear preferential attachment trees. We also show that centrality may be utilized to generate a finite-sized 1-ε confidence set for the root node, for any ε > 0 in a certain subclass of sublinear preferential attachment trees.