Preprint number: CP3-Origins-2017-32 DNRF90

Authors:

We introduce a Markov Chain Monte Carlo algorithm which samples from the space of spanning

trees of complete graphs using local rewiring operations only. The probability distribution of graphs

of this kind is shown to depend on the symmetries of these graphs and these symmetries are reflected

in the equilibrium distribution of the Markov chain. We prove that the algorithm is ergodic and

proceed to estimate the probability distribution for small graph ensembles with exactly known

probabilities. The autocorrelation time of the graph diameter demonstrates that the algorithm

generates independent configurations efficiently as the system size increases. Finally, the mean

graph diameter is estimated for spanning trees of sizes ranging over three orders of magnitude. The

mean graph diameter results agree very closely with asymptotic values.