Notes on the Exponential Random Graph Model: a contribution to the critique of interdisciplinarity

A tutorial discussion is presented about the Exponential Random Graph Model (ERGM) of Social Network Analysis (SNA). The intended audience is post-graduate students and researchers in social science who are curious to understand better where quantitative models come from, for a more effective integration with qualitative methodologies. The discussion is traced back to Jaynes’s distinction between objective and subjective interpretations of probability, where the former emphasizes likelihood of outcomes based on frequency distributions, while the latter emphasizes our incomplete knowledge or uncertainty about the outcome. Although within information theory both views lead to the same functional form for information entropy, when applying these concepts to graph theory the paper shows that the subjective view leads to the ERGM, while the objective view yields a different functional form for the ‘graph entropy’. It is hoped that the critical perspective on interdisciplinarity developed throughout the paper lends credibility and insight to the conclusion that the subjective view of graph entropy is justified as an optimization principle for the most likely distribution of different graph metrics.