Dependence Graphs and Sufficient Statistics

Abstract

Chapter Outline This chapter is written for those interested in a more detailed understanding of how assumptions regarding various forms of dependence can be formalized. What is treated here is not essential for applying exponential random graph models (ERGMs) and may be skipped at a first reading. The general idea, laid down by Frank and Strauss (1986), is nevertheless crucial to the formulation of statistical models treated in this book. Important key points in this chapter are as follows: Subgraph counts are not arbitrarily chosen in ERGMs but correspond to specific dependency structures. The subgraph counts in ERGMs are intricately nested and interdependent, so care has to be taken in in..