Properties of latent variable network models

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

Average path length · Cluster analysis · Clustering coefficient · Combinatorics · Complex network · Degree (music · Degree distribution · Discrete mathematics · Focus (optics · Gaussian · Graph · Latent class model · Latent variable · Latent variable model · Mathematical analysis · Mixture model · Physics · Position (finance · Probabilistic latent semantic analysis · Shortest path problem · Statistical physics · Statistics · Variable (mathematics · Complex Network Analysis Techniques · Computer Science · Mathematics · Mental Health Research Topics · Opinion Dynamics and Social Influence · Artificial Intelligence

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