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.
|Number of pages||47|
|Journal||Journal of Statistical Mechanics: Theory and Experiment|
|Publication status||Published - 9 Apr 2009|
- random graphs
- growth processes
- exact results
David, F., Dukes, M., Jónsson, T., & Stefánsson, S. Ö. (2009). Random tree growth by vertex splitting. Journal of Statistical Mechanics: Theory and Experiment, 2009(4). https://doi.org/10.1088/1742-5468/2009/04/P04009