## Electronic Journal of Statistics

### Exponential-family random graph models for valued networks

Pavel N. Krivitsky

#### 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.

#### Article information

Source
Electron. J. Statist. Volume 6 (2012), 1100-1128.

Dates
First available in Project Euclid: 22 June 2012

http://projecteuclid.org/euclid.ejs/1340369356

Digital Object Identifier
doi:10.1214/12-EJS696

Mathematical Reviews number (MathSciNet)
MR2988440

Zentralblatt MATH identifier
06166989

Subjects
Primary: 91D30: Social networks
Secondary: 60B05: Probability measures on topological spaces

#### Citation

Krivitsky, Pavel N. Exponential-family random graph models for valued networks. Electron. J. Statist. 6 (2012), 1100--1128. doi:10.1214/12-EJS696. http://projecteuclid.org/euclid.ejs/1340369356.

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