  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.
