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Stochastic Evolution of Graphs using Local Moves

Hal Finkel
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Abstract

Inspired by theories such as Loop Quantum Gravity, a class of stochastic graph dynamics was studied in an attempt to gain a better understanding of discrete relational systems under the influence of local dynamics. Unlabeled graphs in a variety of initial configurations were evolved using local rules, similar to Pachner moves, until they reached a size of tens of thousands of vertices. The effect of using different combinations of local moves was studied and a clear relationship can be discerned between the proportions used and the properties of the evolved graphs. Interestingly, simulations suggest that a number of relevant properties possess asymptotic stability with respect to the size of the evolved graphs.

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Hal Finkel. 2006-01-21. Stochastic Evolution of Graphs using Local Moves. https://arxiv.org/abs/hep-th/0601163

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