# Correlated Stochastic Block Models: Exact Graph Matching with Applications to Recovering Communities

@inproceedings{Rcz2021CorrelatedSB, title={Correlated Stochastic Block Models: Exact Graph Matching with Applications to Recovering Communities}, author={Mikl{\'o}s Z. R{\'a}cz and Anirudh Sridhar}, booktitle={Neural Information Processing Systems}, year={2021} }

and held problem-solving sessions for talented middle school students. The sessions were on probability games, based on problem sets that I designed.

## 9 Citations

### Exact Community Recovery in Correlated Stochastic Block Models

- Computer ScienceCOLT
- 2022

A novel algorithm is developed that carefully synthesizes algorithms from the community recovery and graph matching literatures and derives the precise information-theoretic threshold for exact community recovery using multiple correlated graphs.

### Aligning random graphs with a sub-tree similarity message-passing algorithm

- Computer Science, MathematicsJournal of Statistical Mechanics: Theory and Experiment
- 2022

A polynomial time message-passing algorithm devised to solve the inference problem of partially recovering the hidden permutation, in the sparse regime with constant average degrees is studied.

### A polynomial time iterative algorithm for matching Gaussian matrices with non-vanishing correlation

- Computer Science, MathematicsArXiv
- 2022

This work proposes an iterative matching algorithm, which succeeds in polynomial time as long as the correlation between the two Gaussian matrices does not vanish.

### Detection threshold for correlated Erd\H{o}s-R\'enyi graphs via densest subgraphs

- Mathematics
- 2022

The problem of detecting edge correlation between two Erd˝os-R´enyi random graphs on n unlabeled nodes can be formulated as a hypothesis testing problem: under the null hypothesis, the two graphs are…

### Seeded graph matching for the correlated Wigner model via the projected power method

- Computer Science
- 2022

It is proved that PPM works even in regimes of constant σ, thus extending the analysis in (Mao et al., 2021) for the sparse Erd¨os-Renyi model to the (dense) Wigner model.

### Clustered Graph Matching for Label Recovery and Graph Classification

- Computer ScienceArXiv
- 2022

It is demonstrated both in theory and practice that if the graphs come from different network classes, then clustering the networks into classes followed by matching the new graph to cluster-averages can yield higher reputation matching performance than matching to the global average graph.

### Clustering Network Vertices in Sparse Contextual Multilayer Networks

- Computer Science
- 2022

This work establishes that the detection threshold coincides with the threshold for weak recovery of the common community structure using multiple correlated networks and co-variate matrices, and provides a quasi-polynomial time algorithm to estimate the latent communities in the recovery regime.

### A factor model of multilayer network interdependence

- Computer ScienceArXiv
- 2022

This work uses the nonnegative Tucker decomposition (NNTuck) with KL-divergence as an expressive factor model for multilayer networks that naturally generalizes existing methods for stochastic block models of multilayers networks.

### Matching recovery threshold for correlated random graphs

- Computer Science, Mathematics
- 2022

A sharp information-theoretic threshold is established for whether it is possible to correctly match a positive fraction of vertices in a correlated graph G ( n, p).

## References

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### Exact alignment recovery for correlated Erdos Renyi graphs

- Computer Science, MathematicsArXiv
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The information-theoretic threshold for exact recovery is determined, i.e. the conditions under which the entire vertex correspondence can be correctly recovered given unbounded computational resources.

### Consistency Thresholds for the Planted Bisection Model

- Computer Science, MathematicsSTOC
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It is shown that the planted bisection is recoverable asymptotically if and only if with high probability every node belongs to the same community as the majority of its neighbors.

### Impossibility of Partial Recovery in the Graph Alignment Problem

- Computer Science, MathematicsCOLT
- 2021

This work proves an impossibility result for partial recovery in the sparse regime, with constant average degree and correlation, as well as a general bound on the maximal reachable overlap for the correlated Erdős-Rényi model.

### Contextual Stochastic Block Models

- Computer ScienceNeurIPS
- 2018

We provide the first information theoretical tight analysis for inference of latent community structure given a sparse graph along with high dimensional node covariates, correlated with the same…

### Local Algorithms for Block Models with Side Information

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It is shown that local algorithms achieve optimal performance in the above three regimes for the block model with side information, in contrast to the cases of independent sets or a single community in random graphs and to the case of symmetric block models without side information.

### A Concentration of Measure Approach to Correlated Graph Matching

- Computer Science, MathematicsIEEE Journal on Selected Areas in Information Theory
- 2021

This article, graph matching is considered under a stochastic model, where a pair of randomly generated graphs with pairwise correlated edges are to be matched such that given the labeling of the vertices in the first graph, the labels in the second graph are recovered by leveraging the correlation among their edges.

### Complex Graphs and Networks

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Graph theory in the information age Old and new concentration inequalities A generative model--the preferential attachment scheme Duplication models for biological networks Random graphs with given…

### Consistent estimation of dynamic and multi-layer block models

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The asymptotic properties of two estimators for the multi-graph SBM, namely spectral clustering and the maximum-likelihood estimate (MLE), are explored and a variational approximation to the MLE that is computationally feasible for large networks is proposed.

### Efficient random graph matching via degree profiles

- Computer Science, MathematicsProbability Theory and Related Fields
- 2020

This work develops an O ~ ( n d 2 + n 2 ) -time algorithm which perfectly recovers the true vertex correspondence with high probability, provided that the average degree is at least d = \varOmega (\log ^2 n) and the two graphs differ by at most d = O ( log - 2 ( n) ) fraction of edges.