# Phase transition in the detection of modules in sparse networks

@article{Decelle2011PhaseTI, title={Phase transition in the detection of modules in sparse networks}, author={A. Decelle and F. Krzakala and C. Moore and L. Zdeborov{\'a}}, journal={Physical review letters}, year={2011}, volume={107 6}, pages={ 065701 } }

We present an asymptotically exact analysis of the problem of detecting communities in sparse random networks generated by stochastic block models. Using the cavity method of statistical physics and its relationship to belief propagation, we unveil a phase transition from a regime where we can infer the correct group assignments of the nodes to one where these groups are undetectable. Our approach yields an optimal inference algorithm for detecting modules, including both assortative and… Expand

#### Supplemental Presentations

#### Figures and Topics from this paper

#### Paper Mentions

#### 158 Citations

Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications

- Mathematics, Computer Science
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2011

585- PDF

Detectability of macroscopic structures in directed asymmetric stochastic block model.

- Physics, Mathematics
- Physical review. E
- 2019

3- PDF

Community detection in networks: Modularity optimization and maximum likelihood are equivalent

- Computer Science, Physics
- ArXiv
- 2016

66- PDF

Graph spectra and the detectability of community structure in networks

- Computer Science, Physics
- Physical review letters
- 2012

247 Highly Influenced- PDF

An improved belief propagation algorithm for detecting meso-scale structure in complex networks

- Computer Science, Medicine
- Chaos
- 2020

- PDF

Parsimonious module inference in large networks.

- Computer Science, Medicine
- Physical review letters
- 2013

145- PDF

Adapting the Stochastic Block Model to Edge-Weighted Networks

- Computer Science, Mathematics
- ArXiv
- 2013

55- PDF

Computational Complexity, Phase Transitions, and Message-Passing for Community Detection

- Mathematics, Physics
- ArXiv
- 2014

- PDF

#### References

SHOWING 1-10 OF 53 REFERENCES

(Un)detectable cluster structure in sparse networks.

- Computer Science, Medicine
- Physical review letters
- 2008

57- PDF

Stochastic blockmodels and community structure in networks

- Mathematics, Computer Science
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2011

1,328- PDF

Mixture models and exploratory analysis in networks

- Computer Science, Physics
- Proceedings of the National Academy of Sciences
- 2007

493- PDF

A nonparametric view of network models and Newman–Girvan and other modularities

- Medicine
- Proceedings of the National Academy of Sciences
- 2009

621- PDF

Resolution limit in community detection

- Sociology, Environmental Science
- Proceedings of the National Academy of Sciences
- 2007

2,386- PDF

Finding and evaluating community structure in networks.

- Computer Science, Physics
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2004

10,770- PDF

Performance of modularity maximization in practical contexts.

- Mathematics, Physics
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2010

795- PDF