Leaves of preferential attachment trees
Harrison Hartle, P. L. Krapivsky

TL;DR
This paper characterizes the joint distribution of degree and leafdegree in large preferential attachment trees, providing detailed probabilistic descriptions and extending the approach to other models like recursive trees and redirection models.
Contribution
It introduces a comprehensive probabilistic framework for leafdegree statistics in preferential attachment trees, applicable to various models and enabling new tractable analyses.
Findings
Derived the joint degree-leafdegree distribution $n_{k, au}$ from its generating function.
Obtained leafdegree distribution $m_{ au}$ and fraction of protected vertices $n_{k,0}$.
Analyzed fluctuations and concentration of empirical counts $N_{k, au}$.
Abstract
We provide a local probabilistic description of the limiting statistics of large preferential attachment trees in terms of the ordinary degree (number of neighbors) but augmented with information on leafdegree (number of neighbors that are leaves). The full description is the joint degree-leafdegree distribution , which we derive from its associated multivariate generating function. From we obtain the leafdegree distribution, , as well as the fraction of vertices that are protected (nonleaves with leafdegree zero) as a function of degree, , among numerous other results. We also examine fluctuations and concentration of joint degree-leafdegree empirical counts . Although our main findings pertain to the preferential attachment tree, the approach we present is highly generalizable and can characterize numerous existing models, in…
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Taxonomy
TopicsComplex Network Analysis Techniques · Stochastic processes and statistical mechanics · Bayesian Methods and Mixture Models
