Turns out that Cosma has been here very much first.
Jaeger, Manfred, and Oliver Schulte. 2020. “A Complete Characterization of Projectivity for Statistical Relational Models,” April. http://arxiv.org/abs/2004.10984.
Shalizi, Cosma Rohilla, and Alessandro Rinaldo. 2013. “Consistency Under Sampling of Exponential Random Graph Models.” Annals of Statistics 41 (2): 508–35. https://doi.org/10.1214/12-AOS1044.
Snijders, Tom A. B. 2010. “Conditional Marginalization for Exponential Random Graph Models.” The Journal of Mathematical Sociology 34 (4): 239–52. https://doi.org/10.1080/0022250X.2010.485707.