# Properties of Latent Variable Network Models

arXiv: https://arxiv.org/abs/1506.07806 · HTML: https://mlsanity.com/paper/1506.07806/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jun 2015.

## Built on by (most cited first, 4 of 4)

- [Using Embeddings for Causal Estimation of Peer Influence in Social Networks](https://mlsanity.com/paper/2205.08033/) (2022)
- [Continuous Latent Position Models for Instantaneous Interactions](https://mlsanity.com/paper/2103.17146/) (2021)
- [Symphony in the Latent Space: Provably Integrating High-dimensional Techniques with Non-linear Machine Learning Models](https://mlsanity.com/paper/2212.00852/) (2022)
- [Geodesic Length Distribution in Sparse Network Ensembles](https://mlsanity.com/paper/2111.02330/) (2021)

## Abstract (arXiv)

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.