## 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^{-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 ≤ 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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Pages (from-to) | 279-290 |

Number of pages | 12 |

Journal | Random Structures and Algorithms |

Volume | 18 |

Issue number | 3 |

DOIs | |

State | Published - May 2001 |

## ASJC Scopus subject areas

- Software
- General Mathematics
- Computer Graphics and Computer-Aided Design
- Applied Mathematics