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

Fasino, Dario and Tudisco, Francesco (2018) The expected adjacency and modularity matrices in the degree corrected stochastic block model. Special Matrices, 6 (1). pp. 110-121. ISSN 2300-7451

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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.

    • Item type:Article
      ID code:64196
      Dates:
      Date
      Event
      7 March 2018
      Published
      16 February 2018
      Accepted
      Keywords:adjacency matrix, inflation product, modularity matrix, stochastic block model, Probabilities. Mathematical statistics, Algebra and Number Theory, Geometry and Topology
      Subjects:Science > Mathematics > Probabilities. Mathematical statistics
      Department:Faculty of Science > Mathematics and Statistics
      Depositing user: Pure Administrator
      Date deposited:31 May 2018 14:19
      Last modified:09 Sep 2021 02:14
      Related URLs:
      URI:https://strathprints.strath.ac.uk/id/eprint/64196
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