  The literature in social network analysis has largely focused on methods and
models which require complete network data; however there exist many networks
which can only be studied via sampling methods due to the scale or complexity
of the network, access limitations, or the population of interest is hard to
reach. In such cases, the application of random walk-based Markov chain Monte
Carlo (MCMC) methods to estimate multiple network features is common. However,
the reliability of these estimates has been largely ignored. We consider and
further develop multivariate MCMC output analysis methods in the context of
network sampling to directly address the reliability of the multivariate
estimation. This approach yields principled, computationally efficient, and
broadly applicable methods for assessing the Monte Carlo estimation procedure.
In particular, with respect to two random-walk algorithms, a simple random walk
and a Metropolis-Hastings random walk, we construct and compare network
parameter estimates, effective sample sizes, coverage probabilities, and
stopping rules, all of which speaks to the estimation reliability.
