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Properties of Latent Variable Network Models

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SNAW01 - Graph limits and statistics

We derive properties of Latent Variable Models for networks, a broad class of models that includes the widely-used Latent Position Models. We characterise 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 heavy-tailed degree distributions, positive asymptotic clustering coefficients and small-world behaviour 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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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