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

Dario Fasino, Francesco Tudisco

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
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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 languageEnglish
Pages (from-to)110-121
Number of pages12
JournalSpecial Matrices
Volume6
Issue number1
DOIs
Publication statusPublished - 7 Mar 2018

Keywords

  • adjacency matrix
  • inflation product
  • modularity matrix
  • stochastic block model

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