The Degree Sequence of a Scale-Free Random Graph Process [chapter]

Béla Bollobás, Oliver Riordan, Joel Spencer, Gábor Tusnády
2011 The Structure and Dynamics of Networks  
Recently, Barabási and Albert [2] suggested modeling complex real-world networks such as the worldwide web as follows: consider a random graph process in which vertices are added to the graph one at a time and joined to a fixed number of earlier vertices, selected with probabilities proportional to their degrees. In [2] and, with Jeong, in [3], Barabási and Albert suggested that after many steps the proportion P d of vertices with degree d should obey a power law P d α d −γ . They obtained γ =
more » ... They obtained γ = 2 9 ± 0 1 by experiment and gave a simple heuristic argument suggesting that γ = 3. Here we obtain P d asymptotically for all d ≤ n 1/15 , where n is the number of vertices, proving as a consequence that γ = 3.
doi:10.1515/9781400841356.384 fatcat:jhyn5z7hhjfyfimv6b6suyrtfe