### Abstract

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 - 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.

Original language | English (US) |
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Title of host publication | The Structure and Dynamics of Networks |

Publisher | Princeton University Press |

Pages | 385-395 |

Number of pages | 11 |

Volume | 9781400841356 |

ISBN (Electronic) | 9781400841356 |

ISBN (Print) | 0691113572, 9780691113579 |

State | Published - Oct 23 2011 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

*The Structure and Dynamics of Networks*(Vol. 9781400841356, pp. 385-395). Princeton University Press.