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Properties of latent variable network models

Published online by Cambridge University Press:  12 December 2016


RICCARDO RASTELLI
Affiliation:
School of Mathematics and Statistics, University College Dublin, Dublin, Ireland Insight: Centre for Data Analytics, Ireland (e-mail: riccardo.rastelli@ucdconnect.ie; nial.friel@ucd.ie)
NIAL FRIEL
Affiliation:
School of Mathematics and Statistics, University College Dublin, Dublin, Ireland Insight: Centre for Data Analytics, Ireland (e-mail: riccardo.rastelli@ucdconnect.ie; nial.friel@ucd.ie)
ADRIAN E. RAFTERY
Affiliation:
Department of Statistics and Sociology, University of Washington, Seattle, USA (e-mail: raftery@u.washington.edu)

Abstract

We derive properties of latent variable models for networks, a broad class of models that includes the widely used latent position models. We characterize several features of interest, with particular focus on the degree distribution, clustering coefficient, average path length, and degree correlations. We introduce the Gaussian latent position model, and derive analytic expressions and asymptotic approximations for its network properties. We pay particular attention to one special case, the Gaussian latent position model with random effects, and show that it can represent the heavy-tailed degree distributions, positive asymptotic clustering coefficients, and small-world behaviors that often occur in observed social networks. Finally, we illustrate the ability of the models to capture important features of real networks through several well-known datasets.


Type
Research Article
Copyright
Copyright © Cambridge University Press 2016 

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