Mean–variance scaling and stability in commercial sex work networks

Understanding how networks change over time can help identify network properties related to stability and uncover general scaling rules of network evolution. In the analysis of static networks, the tendency of a network to form into modules has received the most support as a measure of network structure and potential stability signature. However, modularity and stability relationships have largely been explored only for networks of information flow (e.g., computer networks) and some bipartite interaction networks (e.g., plant-pollinator networks). We use a collection of over 80 commercial sex worker networks sampled across 18 years to explore the conservation of modularity over time. If modularity is a sign of stability in social or sexual networks, then modular networks should tend to stay modular over time, resulting in a negative mean–variance scaling. We find evidence of positive mean–variance scaling in network size, but a negative mean–variance scaling relationship for modularity. This suggests that commercial sex work networks conserve modularity over time, despite high turnover in the individual nodes (i.e., clients and sex workers) which make up the network. Together, our results link network structure and temporal network dynamics, and provide evidence for clear mean–variance scaling relationships in complex networks.