Conditional Marginalization for Exponential Random Graph Models

Abstract

For exponential random graph models, under quite general conditions, it is proved that induced subgraphs on node sets disconnected from the other nodes still have distributions from an exponential random graph model. This can help in the theoretical interpretation of such models. An application is that for saturated snowball samples from a potentially larger graph which is a realization of an exponential random graph model, it is possible to do the analysis of the observed snowball sample within the framework of exponential random graph models without any knowledge of the larger graph.

Keywords:

• connected component
• network boundary
• network delineation
• random graphs
• snowball sample

This paper was written while being a visiting professorial fellow at the University of Melbourne. I thank Pip Pattison and Garry Robins for stimulating discussions and an anonymous reviewer for comments that led to clarifications.