# Community detection in general stochastic block models: fundamental limits and efficient recovery algorithms

@article{Abbe2015CommunityDI, title={Community detection in general stochastic block models: fundamental limits and efficient recovery algorithms}, author={Emmanuel Abbe and Colin Sandon}, journal={ArXiv}, year={2015}, volume={abs/1503.00609} }

New phase transition phenomena have recently been discovered for the stochastic block model, for the special case of two non-overlapping symmetric communities. This gives raise in particular to new algorithmic challenges driven by the thresholds. This paper investigates whether a general phenomenon takes place for multiple communities, without imposing symmetry.
In the general stochastic block model $\text{SBM}(n,p,Q)$, $n$ vertices are split into $k$ communities of relative size $\{p_i\}_{i…

## 111 Citations

Community Detection in General Stochastic Block models: Fundamental Limits and Efficient Algorithms for Recovery

- Computer Science2015 IEEE 56th Annual Symposium on Foundations of Computer Science
- 2015

This paper investigates the partial and exact recovery of communities in the general SBM (in the constant and logarithmic degree regimes), and uses the generality of the results to tackle overlapping communities.

Density Evolution in the Degree-correlated Stochastic Block Model

- Computer Science, MathematicsCOLT
- 2016

This paper addresses the more refined question of how many vertices that will be misclassified on average under the stochastic block model, and shows that the minimum misclassified fraction on average is attained by a local algorithm, namely belief propagation, in time linear in the number of edges.

Community detection and stochastic block models: recent developments

- Computer ScienceJ. Mach. Learn. Res.
- 2017

The recent developments that establish the fundamental limits for community detection in the stochastic block model are surveyed, both with respect to information-theoretic and computational thresholds, and for various recovery requirements such as exact, partial and weak recovery.

Community Detection and Stochastic Block Models

- Computer ScienceFound. Trends Commun. Inf. Theory
- 2018

The recent developments that establish the fundamental limits for community detection in the stochastic block model are surveyed, both with respect to information-theoretic and computational thresholds, and for various recovery requirements such as exact, partial and weak recovery.

Detection in the stochastic block model with multiple clusters: proof of the achievability conjectures, acyclic BP, and the information-computation gap

- Computer ScienceArXiv
- 2015

The paper proves the efficient detection to non-symmetrical SBMs with a generalized notion of detection and KS threshold, and connects ABP to a power iteration method with a nonbacktracking operator of generalized order, formalizing the interplay between message passing and spectral methods.

Side Information in the Binary Stochastic Block Model: Exact Recovery

- Computer ScienceArXiv
- 2017

An efficient algorithm that incorporates the effect of side information is proposed that uses a partial recovery algorithm combined with a local improvement procedure and sufficient conditions are derived for exact recovery under this efficient algorithm.

Minimax Rates of Community Detection in Stochastic Block Models

- Computer ScienceArXiv
- 2015

A general minimax theory for community detection is provided, which gives minimax rates of the mis-match ratio for a wide rage of settings including homogeneous and inhomogeneous SBMs, dense and sparse networks, finite and growing number of communities.

Relative Density and Exact Recovery in Heterogeneous Stochastic Block Models

- Computer Science
- 2015

It is shown that it is possible, in the right circumstances, to recover very small clusters (up to $\sqrt{\log n}$ size), if there are just a few of them (at most polylogarithmic in $n$).

Multisection in the Stochastic Block Model using Semidefinite Programming

- Computer Science, MathematicsArXiv
- 2015

It is shown that a certain natural SDP-based algorithm solves the problem of exact recovery in the k-community SBM, with high probability, whenever \(\sqrt {\alpha } - \sqRT {\beta } > \sqrt {1}\), as long as \(k=o(\log n)\).

How robust are reconstruction thresholds for community detection?

- Computer ScienceSTOC
- 2016

It is shown that the viewpoint of semirandom models can help explain why some algorithms are preferred to others in practice, in spite of the gaps in their statistical performance on random models, and that algorithms based on semidefinite programming are robust in ways that any algorithm meeting the information-theoretic threshold cannot be.

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