For some user, it may be convenient to simulate random graph with a Gibbs sampler instead of Metropolis-Hastings.
See "Snijders, T. A. B., Pattison, P. E., Robins, G. L., & Handcock, M. S. (2006). New Specifications for Exponential Random Graph Models. Sociological Methodology, 36(1), 99-153. https://doi.org/10.1111/j.1467-9531.2006.00176.x" for references.