Recently, Barabási and Albert  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  and, with Jeong, in , 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-y. 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 ≤ n1/15, where n is the number of vertices, proving as a consequence that γ = 3.
ASJC Scopus subject areas
- Computer Graphics and Computer-Aided Design
- Applied Mathematics