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.

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

Dario Fasino;
2018-01-01

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.
File in questo prodotto:
File Dimensione Formato  
[Special Matrices]2018.pdf

accesso aperto

Descrizione: articolo pubblicato
Tipologia: Versione Editoriale (PDF)
Licenza: Creative commons
Dimensione 877.63 kB
Formato Adobe PDF
877.63 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11390/1129282
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact