# Spectral Algorithms for Community Detection in Directed Networks

arXiv: https://arxiv.org/abs/2008.03820 · HTML: https://mlsanity.com/paper/2008.03820/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Aug 2020.

## Built on by (most cited first, 17 of 17)

- [Community detection for weighted bipartite networks](https://mlsanity.com/paper/2109.10319/) (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)
- [Informative core identification in complex networks](https://mlsanity.com/paper/2101.06388/) (2021)
- [A useful criterion on studying consistent estimation in community detection](https://mlsanity.com/paper/2109.14950/) (2021)
- [Community detection by spectral methods in multi-layer networks](https://mlsanity.com/paper/2403.12540/) (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)
- [Latent class analysis by regularized spectral clustering](https://mlsanity.com/paper/2310.18727/) (2023)
- [Overlapping and nonoverlapping models](https://mlsanity.com/paper/2111.01392/) (2021)
- [Spectral Clustering for Directed Graphs via Likelihood Estimation on Stochastic Block Models](https://mlsanity.com/paper/2403.19516/) (2024)
- [ICEPool: Enhancing Graph Pooling Networks with Inter-cluster Connectivity](https://mlsanity.com/paper/2510.03987/) (2025)
- [Variational Estimators for Node Popularity Models](https://mlsanity.com/paper/2511.17783/) (2025)
- [How many asymmetric communities are there in multi-layer directed networks?](https://mlsanity.com/paper/2602.21569/) (2026)
- [Individual-heterogeneous sub-Gaussian Mixture Models](https://mlsanity.com/paper/2604.05337/) (2026)
- [Exact Community Recovery in Bipartite Networks](https://mlsanity.com/paper/2609.12445/) (2026)

## Abstract (arXiv)

Community detection in large social networks is affected by degree heterogeneity of nodes. The D-SCORE algorithm for directed networks was introduced to reduce this effect by taking the element-wise ratios of the singular vectors of the adjacency matrix before clustering. Meaningful results were obtained for the statistician citation network, but rigorous analysis on its performance was missing. First, this paper establishes theoretical guarantee for this algorithm and its variants for the directed degree-corrected block model (Directed-DCBM). Second, this paper provides significant improvements for the original D-SCORE algorithms by attaching the nodes outside of the community cores using the information of the original network instead of the singular vectors.