Statistics of Lead Changes in Popularity-Driven Systems
Statistical Mechanics
2009-11-07 v2
Abstract
We study statistical properties of the highest degree, or most popular, nodes in growing networks. We show that the number of lead changes increases logarithmically with network size N, independent of the details of the growth mechanism. The probability that the first node retains the lead approaches a finite constant for popularity-driven growth, and decays as N^{-phi}(ln N)^{-1/2}, with phi=0.08607..., for growth with no popularity bias.
Keywords
Cite
@article{arxiv.cond-mat/0207370,
title = {Statistics of Lead Changes in Popularity-Driven Systems},
author = {P. L. Krapivsky and S. Redner},
journal= {arXiv preprint arXiv:cond-mat/0207370},
year = {2009}
}
Comments
4 pages, 4 figures, 2 column revtex format. Minor changes in response to referee comments. For publication in PRL