### 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) |
---|---|

Pages (from-to) | 279-290 |

Number of pages | 12 |

Journal | Random Structures and Algorithms |

Volume | 18 |

Issue number | 3 |

DOIs | |

State | Published - May 2001 |

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### ASJC Scopus subject areas

- Computer Graphics and Computer-Aided Design
- Software
- Mathematics(all)
- Applied Mathematics

### Cite this

*Random Structures and Algorithms*,

*18*(3), 279-290. https://doi.org/10.1002/rsa.1009

**The degree sequence of a scale-free random graph process.** / Bollobás, Béla; Riordan, Oliver; Spencer, Joel; Tusnády, Gábor.

Research output: Contribution to journal › Article

*Random Structures and Algorithms*, vol. 18, no. 3, pp. 279-290. https://doi.org/10.1002/rsa.1009

}

TY - JOUR

T1 - The degree sequence of a scale-free random graph process

AU - Bollobás, Béla

AU - Riordan, Oliver

AU - Spencer, Joel

AU - Tusnády, Gábor

PY - 2001/5

Y1 - 2001/5

N2 - 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 ≤ n1/15, where n is the number of vertices, proving as a consequence that γ = 3.

AB - 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 ≤ n1/15, where n is the number of vertices, proving as a consequence that γ = 3.

UR - http://www.scopus.com/inward/record.url?scp=0035625228&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035625228&partnerID=8YFLogxK

U2 - 10.1002/rsa.1009

DO - 10.1002/rsa.1009

M3 - Article

AN - SCOPUS:0035625228

VL - 18

SP - 279

EP - 290

JO - Random Structures and Algorithms

JF - Random Structures and Algorithms

SN - 1042-9832

IS - 3

ER -