  Exponential random graph models (ERGMs) are widely used for modeling social
networks observed at one point in time. However the computational difficulty of
ERGM parameter estimation has limited the practical application of this class
of models to relatively small networks, up to a few thousand nodes at most,
with usually only a few hundred nodes or fewer. In the case of undirected
networks, snowball sampling can be used to find ERGM parameter estimates of
larger networks via network samples, and recently published improvements in
ERGM network distribution sampling and ERGM estimation algorithms have allowed
ERGM parameter estimates of undirected networks with over one hundred thousand
nodes to be made. However the implementations of these algorithms to date have
been limited in their scalability, and also restricted to undirected networks.
Here we describe an implementation of the recently published Equilibrium
Expectation (EE) algorithm for ERGM parameter estimation of large directed
networks. We test it on some simulated networks, and demonstrate its
application to an online social network with over 1.6 million nodes.
