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Properties of Latent Variable Network Models


Riccardo Rastelli, Nial Friel, Adrian Raftery

Publication Type: 
Refereed Original Article
We derive properties of Latent Variable Models for networks, a broad class of models that includes the widely-used Latent Position Models. These include the average 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 Models with Random Effects, and show that it can represent the heavy-tailed degree distributions, positive asymptotic clustering coefficients and small-world behaviours that are often observed in social networks. Several real and simulated examples illustrate the ability of the models to capture important features of observed networks.
Digital Object Identifer (DOI): 
Publication Status: 
Date Accepted for Publication: 
Saturday, 26 December, 2015
Publication Date: 
Network Science
National University of Ireland, Dublin (UCD)
Open access repository: