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Special Matrices

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The expected adjacency and modularity matrices in the degree corrected stochastic block model

Dario Fasino / Francesco Tudisco
Published Online: 2018-03-07 | DOI: https://doi.org/10.1515/spma-2018-0010


We provide explicit expressions for the eigenvalues and eigenvectors of matrices that can be written as the Hadamard product of a block partitioned matrix with constant blocks and a rank one matrix. Such matrices arise as the expected adjacency or modularity matrices in certain random graph models that are widely used as benchmarks for community detection algorithms.

Keywords: Adjacency matrix; modularity matrix; stochastic block model; inflation product

MSC 2010: 15A18; 15B99


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About the article

Received: 2017-10-20

Accepted: 2018-02-16

Published Online: 2018-03-07

Citation Information: Special Matrices, Volume 6, Issue 1, Pages 110–121, ISSN (Online) 2300-7451, DOI: https://doi.org/10.1515/spma-2018-0010.

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© 2018, published by De Gruyter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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