# Distribution-Free Model for Community Detection

arXiv: https://arxiv.org/abs/2111.07495 · HTML: https://mlsanity.com/paper/2111.07495/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 17 references that are in the map.
- First posted on arXiv 15 Nov 2021.

## Builds on (most cited first, 2 of 2)

- [Regularized Spectral Clustering under the Degree-Corrected Stochastic Blockmodel](https://mlsanity.com/paper/1309.4111/) (2013)
- [Overlapping Clustering Models, and One (class) SVM to Bind Them All](https://mlsanity.com/paper/1806.06945/) (2018)

## Built on by (most cited first, 2 of 2)

- [Bipartite mixed membership distribution-free model. A novel model for community detection in overlapping bipartite weighted networks](https://mlsanity.com/paper/2211.00912/) (2022)
- [Mixed membership distribution-free model](https://mlsanity.com/paper/2112.04389/) (2021)

## Abstract (arXiv)

Community detection for unweighted networks has been widely studied in network analysis, but the case of weighted networks remains a challenge. This paper proposes a general Distribution-Free Model (DFM) for weighted networks in which nodes are partitioned into different communities. DFM can be seen as a generalization of the famous stochastic blockmodels from unweighted networks to weighted networks. DFM does not require prior knowledge of a specific distribution for elements of the adjacency matrix but only the expected value. In particular, signed networks with latent community structures can be modeled by DFM. We build a theoretical guarantee to show that a simple spectral clustering algorithm stably yields consistent community detection under DFM. We also propose a four-step data generation process to generate adjacency matrices with missing edges by combining DFM, noise matrix, and a model for unweighted networks. Using experiments with simulated and real datasets, we show that some benchmark algorithms can successfully recover community membership for weighted networks generated by the proposed data generation process.