  Statistical models for social networks have enabled researchers to study
complex social phenomena that give rise to observed patterns of relationships
among social actors and to gain a rich understanding of the interdependent
nature of social ties and actors. Much of this research has focused on social
networks within medium to large social groups. To date, these advances in
statistical models for social networks, and in particular, of
Exponential-Family Random Graph Models (ERGMS), have rarely been applied to the
study of small networks, despite small network data in teams, families, and
personal networks being common in many fields. In this paper, we revisit the
estimation of ERGMs for small networks and propose using exhaustive enumeration
when possible. We developed an R package that implements the estimation of
pooled ERGMs for small networks using Maximum Likelihood Estimation (MLE),
called "ergmito". Based on the results of an extensive simulation study to
assess the properties of the MLE estimator, we conclude that there are several
benefits of direct MLE estimation compared to approximate methods and that this
creates opportunities for valuable methodological innovations that can be
applied to modeling social networks with ERGMs.
