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 (https://doi.org/10.1515/spma-2018-0010)

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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:28 Mar 2023 09:56
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/64196
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