The cover time of the preferential attachment graph

The preferential attachment graph G m ( 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 [A. Barabási, R. Albert, Emergence of scaling in random networks, Science 286 (1999) 509–512]. In this paper we show that if m ⩾ 2 then whp the cover time of a simple random walk on G m ( n ) is asymptotic to 2 m m − 1 n log n .