# Sparse Popularity Adjusted Stochastic Block Model

arXiv: https://arxiv.org/abs/1910.01931 · HTML: https://mlsanity.com/paper/1910.01931/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Oct 2019.

## Built on by (most cited first, 3 of 3)

- [Network Estimation by Mixing: Adaptivity and More](https://mlsanity.com/paper/2106.02803/) (2021)
- [Sparse Subspace Clustering in Diverse Multiplex Network Model](https://mlsanity.com/paper/2206.07602/) (2022)
- [Strongly Consistent Community Detection in Popularity Adjusted Block Models](https://mlsanity.com/paper/2506.07224/) (2025)

## Abstract (arXiv)

In the present paper we study a sparse stochastic network enabled with a block structure. The popular Stochastic Block Model (SBM) and the Degree Corrected Block Model (DCBM) address sparsity by placing an upper bound on the maximum probability of connections between any pair of nodes. As a result, sparsity describes only the behavior of network as a whole, without distinguishing between the block-dependent sparsity patterns. To the best of our knowledge, the recently introduced Popularity Adjusted Block Model (PABM) is the only block model that allows to introduce a it structural sparsity where some probabilities of connections are identically equal to zero while the rest of them remain above a certain threshold. The latter presents a more nuanced view of the network.