Single-cell transcriptomic data have rapidly become very popular in genomic science. Genomic science also has a long history of using network models to understand the way in which genes work together to carry out specific biological functions. However, working with single-cell data presents major challenges, such as zero inflation and technical noise. These challenges require methods to be specifically adapted to the context of single-cell data. Recently, much effort has been made to develop the theory behind statistical network models. This has lead to many new models being proposed, and has provided a thorough understanding of the properties of existing models. However, a large amount of this work assumes binary-valued relationships between network nodes, whereas genomic network analysis is traditionally based on continuous-valued correlations between genes. In this paper, we assess several established methods for genomic network analysis, we compare ways that these methods can be adapted to the single-cell context, and we use mixture-models to infer binary-valued relationships based on gene-gene correlations. Based on these binary relationships, we find that excellent results can be achieved by using subnetwork analysis methodology popular amongst network statisticians. This methodology thereby allows detection of functional subnetwork modules within these single-cell genomic networks.