The expected adjacency and modularity matrices in the degree corrected stochastic block model-Reference-Cited by-同舟云学术

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

Published:2018-03-07 Issue:1 Volume:6 Page:110-121
ISSN:2300-7451
Container-title:Special Matrices
language:en
Short-container-title:

Author:

Fasino Dario¹,Tudisco Francesco²

Affiliation:

1. Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Università di Udine, Udine , Italy

2. Department of Mathematics and Statistics, University of Strathclyde, Glasgow , UK

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology,Algebra and Number Theory

Link

https://www.degruyter.com/document/doi/10.1515/spma-2018-0010/pdf

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