# Overlapping and nonoverlapping models

arXiv: https://arxiv.org/abs/2111.01392 · HTML: https://mlsanity.com/paper/2111.01392/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 23 references that are in the map.
- First posted on arXiv 2 Nov 2021.

## Builds on (most cited first, 12 of 12)

- [Consistency of spectral clustering in stochastic block models](https://mlsanity.com/paper/1312.2050/) (2013)
- [Regularized Spectral Clustering under the Degree-Corrected Stochastic Blockmodel](https://mlsanity.com/paper/1309.4111/) (2013)
- [Impact of regularization on Spectral Clustering](https://mlsanity.com/paper/1312.1733/) (2013)
- [Detecting Overlapping Communities in Networks Using Spectral Methods](https://mlsanity.com/paper/1412.3432/) (2014)
- [Estimating Mixed Memberships with Sharp Eigenvector Deviations](https://mlsanity.com/paper/1709.00407/) (2017)
- [Analysis of spectral clustering algorithms for community detection: the general bipartite setting](https://mlsanity.com/paper/1803.04547/) (2018)
- [Spectral Algorithms for Community Detection in Directed Networks](https://mlsanity.com/paper/2008.03820/) (2020)
- [Semidefinite Programming Based Preconditioning for More Robust Near-Separable Nonnegative Matrix Factorization](https://mlsanity.com/paper/1310.2273/) (2013)
- [Overlapping Clustering Models, and One (class) SVM to Bind Them All](https://mlsanity.com/paper/1806.06945/) (2018)
- [A useful criterion on studying consistent estimation in community detection](https://mlsanity.com/paper/2109.14950/) (2021)
- [Directed mixed membership stochastic blockmodel](https://mlsanity.com/paper/2101.02307/) (2021)
- [Directed degree corrected mixed membership model and estimating community memberships in directed networks](https://mlsanity.com/paper/2109.07826/) (2021)

## Abstract (arXiv)

Consider a directed network with Kr row communities and Kc column communities. Previous works found that modeling directed networks in which all nodes have overlapping property requires Kr=Kc for identifiability. In this paper, we propose an overlapping and nonoverlapping model to study directed networks in which row nodes have overlapping property while column nodes do not. The proposed model is identifiable when Kr≤ Kc. Meanwhile, we provide one identifiable model as extension of ONM to model directed networks with variation in node degree. Two spectral algorithms with theoretical guarantee on consistent estimations are designed to fit the models. A small scale of numerical studies are used to illustrate the algorithms.