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Random Structures and Algorithms
Article . 2026 . Peer-reviewed
License: CC BY
Data sources: Crossref
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https://dx.doi.org/10.48550/ar...
Article . 2024
License: arXiv Non-Exclusive Distribution
Data sources: Datacite
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Random Friend Trees

Authors: Louigi Addario‐Berry; Simon Briend; Luc Devroye; Serte Donderwinkel; Céline Kerriou; Gábor Lugosi;

Random Friend Trees

Abstract

ABSTRACT We study a random recursive tree model featuring complete redirection called the random friend tree and introduced by Saramäki and Kaski (2004). Vertices are attached sequentially, one by one, by selecting an existing target vertex and connecting to one of its neighbours (or friends), chosen uniformly at random. This model has interesting emergent properties, such as a highly skewed degree sequence. In contrast to the preferential attachment model, these emergent phenomena stem from a local rather than a global attachment mechanism. The structure of the resulting tree is also strikingly different from both the preferential attachment tree and the uniform random recursive tree: every edge is incident to a macro‐hub of asymptotically linear degree, and with high probability all but at most vertices in a tree of size are leaves. We prove various results on the neighbourhood of fixed vertices and edges, and we study macroscopic properties such as the diameter and the degree distribution, providing insights into the overall structure of the tree. We also present a number of open questions on this model and related models.

Keywords

60C05 60J80 05C05, Probability (math.PR), FOS: Mathematics, Mathematics - Probability

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green