# Community Detection via Random and Adaptive Sampling

arXiv: https://arxiv.org/abs/1402.3072 · HTML: https://mlsanity.com/paper/1402.3072/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2014.

## Built on by (most cited first, 7 of 7)

- [Semidefinite Programming for Community Detection with Side Information](https://mlsanity.com/paper/2105.02816/) (2021)
- [Community Detection: Exact Recovery in Weighted Graphs](https://mlsanity.com/paper/2102.04439/) (2021)
- [Community Detection with Known, Unknown, or Partially Known Auxiliary Latent Variables](https://mlsanity.com/paper/2301.04088/) (2023)
- [Near-Optimal Clustering in Mixture of Markov Chains](https://mlsanity.com/paper/2506.01324/) (2025)
- [Dynamic Network Sampling for Community Detection](https://mlsanity.com/paper/2208.13921/) (2022)
- [Revisiting Instance-Optimal Cluster Recovery in the Labeled Stochastic Block Model](https://mlsanity.com/paper/2306.12968/) (2023)
- [Query-Limited Community Recovery in Stochastic Block Models](https://mlsanity.com/paper/2606.02055/) (2026)

## Abstract (arXiv)

In this paper, we consider networks consisting of a finite number of non-overlapping communities. To extract these communities, the interaction between pairs of nodes may be sampled from a large available data set, which allows a given node pair to be sampled several times. When a node pair is sampled, the observed outcome is a binary random variable, equal to 1 if nodes interact and to 0 otherwise. The outcome is more likely to be positive if nodes belong to the same communities. For a given budget of node pair samples or observations, we wish to jointly design a sampling strategy (the sequence of sampled node pairs) and a clustering algorithm that recover the hidden communities with the highest possible accuracy. We consider both non-adaptive and adaptive sampling strategies, and for both classes of strategies, we derive fundamental performance limits satisfied by any sampling and clustering algorithm. In particular, we provide necessary conditions for the existence of algorithms recovering the communities accurately as the network size grows large. We also devise simple algorithms that accurately reconstruct the communities when this is at all possible, hence proving that the proposed necessary conditions for accurate community detection are also sufficient. The classical problem of community detection in the stochastic block model can be seen as a particular instance of the problems consider here. But our framework covers more general scenarios where the sequence of sampled node pairs can be designed in an adaptive manner. The paper provides new results for the stochastic block model, and extends the analysis to the case of adaptive sampling.