# Detecting Overlapping Communities in Networks Using Spectral Methods

arXiv: https://arxiv.org/abs/1412.3432 · HTML: https://mlsanity.com/paper/1412.3432/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Dec 2014.

## Built on by (most cited first, 22 of 22)

- [Curvature-based Clustering on Graphs](https://mlsanity.com/paper/2307.10155/) (2023)
- [Latent Space Model for Higher-order Networks and Generalized Tensor Decomposition](https://mlsanity.com/paper/2106.16042/) (2021)
- [Consistency of Constrained Spectral Clustering under Graph Induced Fair Planted Partitions](https://mlsanity.com/paper/2105.03714/) (2021)
- [Community detection for weighted bipartite networks](https://mlsanity.com/paper/2109.10319/) (2021)
- [Community Detection in the Stochastic Block Model by Mixed Integer Programming](https://mlsanity.com/paper/2101.12336/) (2021)
- [Bipartite mixed membership distribution-free model. A novel model for community detection in overlapping bipartite weighted networks](https://mlsanity.com/paper/2211.00912/) (2022)
- [Network Representation Learning: From Traditional Feature Learning to Deep Learning](https://mlsanity.com/paper/2103.04339/) (2021)
- [A useful criterion on studying consistent estimation in community detection](https://mlsanity.com/paper/2109.14950/) (2021)
- [Improved Algorithm and Bounds for Successive Projection](https://mlsanity.com/paper/2403.11013/) (2024)
- [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)
- [Mixed membership distribution-free model](https://mlsanity.com/paper/2112.04389/) (2021)
- [Variational Estimators of the Degree-corrected Latent Block Model for Bipartite Networks](https://mlsanity.com/paper/2206.08465/) (2022)
- [A pseudo-likelihood approach to community detection in weighted networks](https://mlsanity.com/paper/2303.05909/) (2023)
- [Optimal Variable Clustering for High-Dimensional Matrix Valued Data](https://mlsanity.com/paper/2112.12909/) (2021)
- [Overlapping and nonoverlapping models](https://mlsanity.com/paper/2111.01392/) (2021)
- [On consistency of constrained spectral clustering under representation-aware stochastic block model](https://mlsanity.com/paper/2203.02005/) (2022)
- [Selecting the Number of Communities for Weighted Degree-Corrected Stochastic Block Models](https://mlsanity.com/paper/2406.05340/) (2024)
- [A Spectral Framework for Tracking Communities in Evolving Networks](https://mlsanity.com/paper/2412.07378/) (2024)
- [Generalized Grade-of-Membership Estimation for High-dimensional Locally Dependent Data](https://mlsanity.com/paper/2412.19796/) (2024)
- [Semi-supervised Vertex Hunting, with Applications in Network and Text Analysis](https://mlsanity.com/paper/2510.22526/) (2025)
- [Adjacency Spectral Embeddings of Correlation Networks](https://mlsanity.com/paper/2602.21055/) (2026)

## Abstract (arXiv)

Community detection is a fundamental problem in network analysis which is made more challenging by overlaps between communities which often occur in practice. Here we propose a general, flexible, and interpretable generative model for overlapping communities, which can be thought of as a generalization of the degree-corrected stochastic block model. We develop an efficient spectral algorithm for estimating the community memberships, which deals with the overlaps by employing the K-medians algorithm rather than the usual K-means for clustering in the spectral domain. We show that the algorithm is asymptotically consistent when networks are not too sparse and the overlaps between communities not too large. Numerical experiments on both simulated networks and many real social networks demonstrate that our method performs very well compared to a number of benchmark methods for overlapping community detection.