# Latent Poisson models for networks with heterogeneous density

arXiv: https://arxiv.org/abs/2002.07803 · HTML: https://mlsanity.com/paper/2002.07803/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Feb 2020.

## Built on by (most cited first, 5 of 5)

- [Disentangling homophily, community structure and triadic closure in networks](https://mlsanity.com/paper/2101.02510/) (2021)
- [Systematic assessment of the quality of fit of the stochastic block model for empirical networks](https://mlsanity.com/paper/2201.01658/) (2022)
- [Echo-chambers and Idea Labs: Communication Styles on Twitter](https://mlsanity.com/paper/2403.19423/) (2024)
- [Uncertainty quantification and posterior sampling for network reconstruction](https://mlsanity.com/paper/2503.07736/) (2025)
- [Knowledge Graph Representation for Political Information Sources](https://mlsanity.com/paper/2404.03437/) (2024)

## Abstract (arXiv)

Empirical networks are often globally sparse, with a small average number of connections per node, when compared to the total size of the network. However, this sparsity tends not to be homogeneous, and networks can also be locally dense, for example with a few nodes connecting to a large fraction of the rest of the network, or with small groups of nodes with a large probability of connections between them. Here we show how latent Poisson models which generate hidden multigraphs can be effective at capturing this density heterogeneity, while being more tractable mathematically than some of the alternatives that model simple graphs directly. We show how these latent multigraphs can be reconstructed from data on simple graphs, and how this allows us to disentangle disassortative degree-degree correlations from the constraints of imposed degree sequences, and to improve the identification of community structure in empirically relevant scenarios.