Stochastic Evolution of Graphs using Local Moves
Abstract
Description
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.
17 pages, 17 figures. Basis for talk given at the LOOPS'05 conference (Potsdam, Germany: 13 Oct. 2005)
17 pages, 17 figures. Basis for talk given at the LOOPS'05 conference (Potsdam, Germany: 13 Oct. 2005)