### Abstract

We analyze an evolving network model of Krapivsky and Redner in which new nodes arrive sequentially, each connecting to a previously existing node b with probability proportional to the pth power of the in-degree of b. We restrict to the super-linear case p > 1. When (Formula presented), the structure of the final countable tree is determined. There is a finite tree T with distinguished v (which has a limiting distribution) on which is “glued” a specific infinite tree; v has an infinite number of children, an infinite number of which have k − 1 children, and there are only a finite number of nodes (possibly only v) with k or more children. Our basic technique is to embed the discrete process in a continuous time process using exponential random variables, a technique that has previously been employed in the study of balls-in-bins processes with feedback.

Original language | English (US) |
---|---|

Pages (from-to) | 121-163 |

Number of pages | 43 |

Journal | Internet Mathematics |

Volume | 2 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 2005 |

### ASJC Scopus subject areas

- Modeling and Simulation
- Computational Mathematics
- Applied Mathematics

## Fingerprint Dive into the research topics of 'Connectivity transitions in networks with super-linear preferential attachment'. Together they form a unique fingerprint.

## Cite this

*Internet Mathematics*,

*2*(2), 121-163. https://doi.org/10.1080/15427951.2005.10129101