# Exponential random graph model parameter estimation for very large directed networks

## TL;DR

This paper presents a scalable implementation of the Equilibrium Expectation algorithm for ERGM parameter estimation in large directed networks, enabling analysis of networks with over a million nodes.

## Contribution

It introduces a new scalable method for ERGM parameter estimation specifically for large directed networks, extending previous work limited to undirected networks.

## Key findings

- Successfully applied to a network with 1.6 million nodes
- Demonstrates scalability of the EE algorithm for directed networks
- Provides a practical tool for large-scale social network analysis

## Abstract

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.

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Source: https://tomesphere.com/paper/1904.08063