Stable Exponential Random Graph Models with Non-parametric Components   for Large Dense Networks
  Exponential Random Graph Models (ERGM) behave peculiar in large networks with thousand(s) of actors (nodes). Standard models containing two-star or triangle counts as statistics are often unstable leading to completely full or empty networks. Moreover, numerical methods break down which makes it complicated to apply ERGMs to large networks. In this paper we propose two strategies to circumvent these obstacles. First, we fit a model to a subsampled network and secondly, we show how linear statistics (like two-stars etc.) can be replaced by smooth functional components. These two steps in combination allow to fit stable models to large network data, which is illustrated by a data example including a residual analysis. 
Stephanie Thiemichen and G\"oran Kauermann
stat.AP stat.ME