On the interpretability of thresholded social networks

Understanding the factors of network formation is a fundamental aspect in the study of social dynamics. Online activity provides us with abundance of data that allows us to reconstruct and study social networks. Statistical inference methods are often used to study network formation. Ideally, statistical inference allows the researcher to study the significance of specific factors to the network formation. One popular framework is known as Exponential Random Graph Models (ERGM) which provides principled and statistically sound interpretation of an observed network structure. Networks, however, are not always given set in stone. Often times, the network is "reconstructed" by applying some thresholds on the observed data/signals. We show that subtle changes in the thresholding have significant effects on the ERGM results, casting doubts on the interpretability of the model. In this work we present a case study in which different thresholding techniques yield radically different results that lead to contrastive interpretations. Consequently, we revisit the applicability of ERGM to thresholded networks.