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

[thumbnail of Fasino-Tudisco-SM-2018-The-expected-adjacency-and-modularity-matrices-in-the-degree-corrected]

Preview

Text (Fasino-Tudisco-SM-2018-The-expected-adjacency-and-modularity-matrices-in-the-degree-corrected)
Fasino_Tudisco_SM_2018_The_expected_adjacency_and_modularity_matrices_in_the_degree_corrected.pdf
Final Published Version
License:

Download (857kB)| Preview

Official URL: https://doi.org/10.1515/spma-2018-0010

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.

Citations and altmetrics

Item metadata

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:	04 Jun 2021 00:38
Related URLs:	Scopus publication
URI:	https://strathprints.strath.ac.uk/id/eprint/64196

Export

CORE (COnnecting REpositories)