### Abstract

Language | English |
---|---|

Number of pages | 47 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2009 |

Issue number | 4 |

DOIs | |

Publication status | Published - 9 Apr 2009 |

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### Keywords

- random graphs
- networks
- growth processes
- exact results

### Cite this

*Journal of Statistical Mechanics: Theory and Experiment*,

*2009*(4). https://doi.org/10.1088/1742-5468/2009/04/P04009

}

*Journal of Statistical Mechanics: Theory and Experiment*, vol. 2009, no. 4. https://doi.org/10.1088/1742-5468/2009/04/P04009

**Random tree growth by vertex splitting.** / David, François; Dukes, Mark; Jónsson, Thordur; Stefánsson, Sigurdur Örn.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Random tree growth by vertex splitting

AU - David, François

AU - Dukes, Mark

AU - Jónsson, Thordur

AU - Stefánsson, Sigurdur Örn

PY - 2009/4/9

Y1 - 2009/4/9

N2 - We study a model of growing planar tree graphs where in each time step we separate the tree into two components by splitting a vertex and then connect the two pieces by inserting a new link between the daughter vertices. This model generalizes the preferential attachment model and Ford's α-model for phylogenetic trees. We develop a mean field theory for the vertex degree distribution, prove that the mean field theory is exact in some special cases and check that it agrees with numerical simulations in general. We calculate various correlation functions and show that the intrinsic Hausdorff dimension can vary from 1 to ∞, depending on the parameters of the model.

AB - We study a model of growing planar tree graphs where in each time step we separate the tree into two components by splitting a vertex and then connect the two pieces by inserting a new link between the daughter vertices. This model generalizes the preferential attachment model and Ford's α-model for phylogenetic trees. We develop a mean field theory for the vertex degree distribution, prove that the mean field theory is exact in some special cases and check that it agrees with numerical simulations in general. We calculate various correlation functions and show that the intrinsic Hausdorff dimension can vary from 1 to ∞, depending on the parameters of the model.

KW - random graphs

KW - networks

KW - growth processes

KW - exact results

U2 - 10.1088/1742-5468/2009/04/P04009

DO - 10.1088/1742-5468/2009/04/P04009

M3 - Article

VL - 2009

JO - Journal of Statistical Mechanics: Theory and Experiment

T2 - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

IS - 4

ER -