Special Matrices (Mar 2018)

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

  • Fasino Dario,
  • Tudisco Francesco

DOI
https://doi.org/10.1515/spma-2018-0010
Journal volume & issue
Vol. 6, no. 1
pp. 110 – 121

Abstract

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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.

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