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-γ. 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.
|Original language||English (US)|
|Title of host publication||The Structure and Dynamics of Networks|
|Publisher||Princeton University Press|
|Number of pages||11|
|ISBN (Print)||0691113572, 9780691113579|
|State||Published - Oct 23 2011|
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