David, François and Dukes, Mark and Jónsson, Thordur and Stefánsson, Sigurdur Örn (2009) Random tree growth by vertex splitting. Journal of Statistical Mechanics: Theory and Experiment, 2009 (4). ISSN 1742-5468Full text not available in this repository. (Request a copy from the Strathclyde author)
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.
|Keywords:||random graphs, networks, growth processes, exact results, Mathematics, Statistical and Nonlinear Physics, Statistics and Probability, Statistics, Probability and Uncertainty|
|Subjects:||Science > Mathematics|
|Department:||Faculty of Science > Computer and Information Sciences|
|Depositing user:||Pure Administrator|
|Date Deposited:||19 Oct 2011 10:31|
|Last modified:||22 Mar 2017 11:44|