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- W2331611075 abstract "We consider a preferential attachment network growth process under a simple linear dynamic: vertices are added to the network one at a time, and at stage $t$ the probability that the new $t+1$st vertex connects to vertex $u leq t$ is exactly $frac{d_u(t)}{t}$ where $d_u(t)$ is the degree of $u$ at time $t$. Building on some Martingale machinery introduced by Kleinberg and Kleinberg in [9], we show that, so long as the initial graph is neither edgeless nor complete, with probability 1 the infinite limit of the process will be a copy of the Rado graph augmented with a finite number of either isolated or universal vertices. Finally, we offer an informal argument that this result does not generalise to processes with attachment probability $lambda cdot frac{d_u(t)}{t}$ where $lambda <1$." @default.
- W2331611075 created "2016-06-24" @default.
- W2331611075 creator A5067853307 @default.
- W2331611075 date "2016-03-29" @default.
- W2331611075 modified "2023-09-27" @default.
- W2331611075 title "A Linear Preferential Attachment Process Approaching the Rado Graph" @default.
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