Non-convergence of proportions of types in a preferential attachment graph with three co-existing types

Electronic Communications in Probability

John Haslegrave¹ 

关键词: preferential attachment;    stochastic approximation;    social networks;    competing types;   

DOI  :  10.1214/18-ECP157

学科分类：统计和概率

来源: Institute of Mathematical Statistics

【 摘 要 】

We consider the preferential attachment model with multiple vertex types introduced by Antunović, Mossel and Rácz. We give an example with three types, based on the game of rock-paper-scissors, where the proportions of vertices of the different types almost surely do not converge to a limit, giving a counterexample to a conjecture of Antunović, Mossel and Rácz. We also consider another family of examples where we show that the conjecture does hold.

【 授权许可】

CC BY