Prove convergence of the MCMC edge-swapping null-model sampler

Establish convergence guarantees for the Markov chain induced by the MCMC edge-swapping algorithm used to generate randomized interaction networks that preserve degree sequences for toxicity analysis, and ascertain swap counts (e.g., as a function of |E|) sufficient to approach stationarity under the study’s sampling protocol.

Background

To compare empirical toxicity levels with a null expectation, the paper samples 100 randomized interaction networks via an MCMC edge-swapping procedure that preserves degree sequences (and toxicity distribution). Randomization is performed by executing Q·|E| endpoint swaps, with Q set conservatively to log|E|.

The authors explicitly state that there is no definite proof of convergence for this Markov chain under their setup. A formal convergence proof and swap-complexity bounds would validate the null-model sampling rigor and support the robustness of toxicity comparisons.