Stable Exponential Random Graph Models with Non-parametric Components for Large Dense Networks

TL;DR

This paper introduces methods to stabilize and efficiently fit exponential random graph models to large dense networks by using subsampling and smooth functional components, overcoming previous computational and stability issues.

Contribution

It proposes two novel strategies—subsampling and replacing linear statistics with smooth functions—to enable stable ERGM fitting for large networks.

Findings

Stable models successfully fitted to large networks

Subsampling reduces computational complexity

Smooth components improve model stability

Abstract

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.