Estimates of population size for hidden and hard-to-reach individuals are of particular interest to health officials when health problems are concentrated in such populations. Efforts to derive these estimates are often frustrated by a range of factors including social stigma or an association with illegal activities that ordinarily preclude conventional survey strategies. This paper builds on and extends prior work that proposed a method to meet these challenges. Here we describe a rigorous formalization of a one-step, network-based population estimation procedure that can be employed under conditions of anonymity. The estimation procedure is designed to be implemented alongside currently accepted strategies for research with hidden populations. Simulation experiments are described that test the efficacy of the method across a range of implementation conditions and hidden population sizes. The results of these experiments show that reliable population estimates can be derived for hidden, networked population as large as 12,500 and perhaps larger for one family of random graphs. As such, the method shows potential for cost-effective implementation health and disease surveillance officials concerned with hidden populations. Limitations and future work are discussed in the concluding section.