### Abstract

Original language | English |
---|---|

Pages (from-to) | 21-40 |

Number of pages | 20 |

Journal | Jahresberichte der Deutschen Mathematiker Vereinigung |

Volume | 113 |

Issue number | 1 |

Publication status | Published - 2011 |

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### Cite this

*Jahresberichte der Deutschen Mathematiker Vereinigung*,

*113*(1), 21-40.

**Random networks with concave preferential attachment rule.** / Dereich, Steffen; Morters, Peter.

Research output: Contribution to journal › Article

*Jahresberichte der Deutschen Mathematiker Vereinigung*, vol. 113, no. 1, pp. 21-40.

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TY - JOUR

T1 - Random networks with concave preferential attachment rule

AU - Dereich, Steffen

AU - Morters, Peter

PY - 2011

Y1 - 2011

N2 - Many of the phenomena in the complex world in which we live have a rough description as a large network of interacting components. Random network theory tries to describe the global structure of such networks from basic local prin- ciples. One such principle is the preferential attachment paradigm which suggests that networks are built by adding nodes and links successively, in such a way that new nodes prefer to be connected to existing nodes if they have a high degree. Our research gives the first comprehensive and mathematically rigorous treatment of the case when this preference follows a nonlinear, or more precisely concave, rule. We survey results obtained so far and some ongoing developments.

AB - Many of the phenomena in the complex world in which we live have a rough description as a large network of interacting components. Random network theory tries to describe the global structure of such networks from basic local prin- ciples. One such principle is the preferential attachment paradigm which suggests that networks are built by adding nodes and links successively, in such a way that new nodes prefer to be connected to existing nodes if they have a high degree. Our research gives the first comprehensive and mathematically rigorous treatment of the case when this preference follows a nonlinear, or more precisely concave, rule. We survey results obtained so far and some ongoing developments.

M3 - Article

VL - 113

SP - 21

EP - 40

JO - Jahresberichte der Deutschen Mathematiker Vereinigung

JF - Jahresberichte der Deutschen Mathematiker Vereinigung

IS - 1

ER -