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.

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