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

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.

Please cite this work as:

@article{fasino2018expected,
  title={The expected adjacency and modularity matrices in the degree corrected stochastic block model},
  author={Fasino, Dario and Tudisco, Francesco},
  journal={Special Matrices},
  volume={6},
  pages={110--121},
  year={2018}
}

Keywords: Adjacency matrix modularity matrix networks stochastic block model inflation product graph modularity