Exponential-Family Random Graph Models for Valued Networks

TL;DR

This paper extends exponential-family random graph models (ERGMs) to valued networks with count data, enabling more accurate modeling of complex social network features without losing information through dichotomization.

Contribution

It introduces a generalized ERGM framework for valued networks, specifically modeling counts, and discusses challenges and solutions for analyzing such data.

Findings

Successfully modeled count-based social networks.

Demonstrated advantages over binary ERGMs.

Applied methods to real-world count interaction data.

Abstract

Exponential-family random graph models (ERGMs) provide a principled and flexible way to model and simulate features common in social networks, such as propensities for homophily, mutuality, and friend-of-a-friend triad closure, through choice of model terms (sufficient statistics). However, those ERGMs modeling the more complex features have, to date, been limited to binary data: presence or absence of ties. Thus, analysis of valued networks, such as those where counts, measurements, or ranks are observed, has necessitated dichotomizing them, losing information and introducing biases. In this work, we generalize ERGMs to valued networks. Focusing on modeling counts, we formulate an ERGM for networks whose ties are counts and discuss issues that arise when moving beyond the binary case. We introduce model terms that generalize and model common social network features for such data and apply these methods to a network dataset whose values are counts of interactions.