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BY-NC-ND 4.0 license Open Access Published by De Gruyter Open Access March 7, 2018

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

  • Dario Fasino and Francesco Tudisco EMAIL logo
From the journal Special Matrices

Abstract

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.

MSC 2010: 15A18; 15B99

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Received: 2017-10-20
Accepted: 2018-02-16
Published Online: 2018-03-07

© 2018, published by De Gruyter

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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