# Mixed Membership Estimation for Social Networks

arXiv: https://arxiv.org/abs/1708.07852 · HTML: https://mlsanity.com/paper/1708.07852/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Aug 2017.

## Built on by (most cited first, 21 of 21)

- [Estimating Higher-Order Mixed Memberships via the ℓ2,∞ Tensor Perturbation Bound](https://mlsanity.com/paper/2212.08642/) (2022)
- [Bipartite mixed membership distribution-free model. A novel model for community detection in overlapping bipartite weighted networks](https://mlsanity.com/paper/2211.00912/) (2022)
- [Improved Algorithm and Bounds for Successive Projection](https://mlsanity.com/paper/2403.11013/) (2024)
- [On the Robustness of the Successive Projection Algorithm](https://mlsanity.com/paper/2411.16195/) (2024)
- [Directed mixed membership stochastic blockmodel](https://mlsanity.com/paper/2101.02307/) (2021)
- [Mixed membership distribution-free model](https://mlsanity.com/paper/2112.04389/) (2021)
- [Mixed membership estimation for categorical data with weighted responses](https://mlsanity.com/paper/2310.10989/) (2023)
- [Inferences on Mixing Probabilities and Ranking in Mixed-Membership Models](https://mlsanity.com/paper/2308.14988/) (2023)
- [Strongly Consistent Community Detection in Popularity Adjusted Block Models](https://mlsanity.com/paper/2506.07224/) (2025)
- [Matrix Factorization Framework for Community Detection under the Degree-Corrected Block Model](https://mlsanity.com/paper/2601.06262/) (2026)
- [Estimating mixed memberships in multi-layer networks](https://mlsanity.com/paper/2404.03916/) (2024)
- [Generalized Grade-of-Membership Estimation for High-dimensional Locally Dependent Data](https://mlsanity.com/paper/2412.19796/) (2024)
- [LOD: Latent Objective Discovery in Heterogeneous Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2505.09756/) (2025)
- [A Transfer Learning Framework for Multilayer Networks via Model Averaging](https://mlsanity.com/paper/2506.12455/) (2025)
- [Semi-supervised Vertex Hunting, with Applications in Network and Text Analysis](https://mlsanity.com/paper/2510.22526/) (2025)
- [DCMM-Transformer: Degree-Corrected Mixed-Membership Attention for Medical Imaging](https://mlsanity.com/paper/2511.12047/) (2025)
- [Adjacency Spectral Embeddings of Correlation Networks](https://mlsanity.com/paper/2602.21055/) (2026)
- [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)
- [Population-Level Generative Modeling for Ranking Data](https://mlsanity.com/paper/2608.08422/) (2026)
- [Degree-Corrected Joint Matrix Factorization for Multilayer Community Detection](https://mlsanity.com/paper/2610.01361/) (2026)

## Abstract (arXiv)

In economics and social science, network data are regularly observed, and a thorough understanding of the network community structure facilitates the comprehension of economic patterns and activities. Consider an undirected network with n nodes and K communities. We model the network using the Degree-Corrected Mixed-Membership (DCMM) model, where for each node i, there exists a membership vector πi = (πi(1), πi(2), ldots, πi(K))', where πi(k) is the weight that node i puts in community k, 1 ≤ k ≤ K. In comparison to the well-known stochastic block model (SBM), the DCMM permits both severe degree heterogeneity and mixed memberships, making it considerably more realistic and general. We present an efficient approach, Mixed-SCORE, for estimating the mixed membership vectors of all nodes and the other DCMM parameters. This approach is inspired by the discovery of a delicate simplex structure in the spectral domain. We derive explicit error rates for the Mixed-SCORE algorithm and demonstrate that it is rate-optimal over a broad parameter space. Our findings provide a novel statistical tool for network community analysis, which can be used to understand network formations, extract nodal features, identify unobserved covariates in dyadic regressions, and estimate peer effects. We applied Mixed-SCORE to a political blog network, two trade networks, a co-authorship network, and a citee network, and obtained interpretable results.