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Abstract
We provide explicit expressions for the eigenvalues andeigenvectors of matrices that can be written as the Hadamard product of a blockpartitioned matrix with constant blocks and a rank one matrix. Such matricesarise as the expected adjacency or modularity matrices in certain random graphmodels that are widely used as benchmarks for community detection algorithms.
Original language | English |
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Pages (from-to) | 110-121 |
Number of pages | 12 |
Journal | Special Matrices |
Volume | 6 |
Issue number | 1 |
DOIs | |
Publication status | Published - 7 Mar 2018 |
Keywords
- adjacency matrix
- inflation product
- modularity matrix
- stochastic block model
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Dive into the research topics of 'The expected adjacency and modularity matrices in the degree corrected stochastic block model'. Together they form a unique fingerprint.Projects
- 1 Finished
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Models and Algorithms for Graph centrality (MAGNET) H2020 MSCA-IF-2016
Higham, D. (Principal Investigator)
European Commission - Horizon Europe + H2020
1/07/17 → 30/06/19
Project: Research Fellowship