The cover time of the preferential attachment graph

The preferential attachment graph Gm(n) is a random graph formed by adding a new vertex at each time step, with m edges which point to vertices selected at random with probability proportional to their degree. Thus at time n there are n vertices and mn edges. This process yields a graph which has been proposed as a simple model of the world wide web [2]. In this paper we show that if m ≥ 2 then whp the cover time of a simple random walk on Gm(n) is asymptotic to 2m m−1n log n.

• Type: Journal
• Year: 2007
• Where: JCT
• Authors: Colin Cooper, Alan M. Frieze
• Keywords: JCT 2007, Preferential Attachment Graph, Random Graph, World Wide Web