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

Title of host publication | The Structure and Dynamics of Networks |

Publisher | Princeton University Press |

Pages | 385-395 |

Number of pages | 11 |

ISBN (Print) | 9781400841356, 0691113572, 9780691113579 |

State | Published - Oct 23 2011 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

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

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

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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

}

TY - CHAP

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

AU - Bollobás, Béla

AU - Riordan, Oliver

AU - Spencer, Joel

AU - Tusnády, Gábor

PY - 2011/10/23

Y1 - 2011/10/23

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-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.

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-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.

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M3 - Chapter

SN - 9781400841356

SN - 0691113572

SN - 9780691113579

SP - 385

EP - 395

BT - The Structure and Dynamics of Networks

PB - Princeton University Press

ER -