Algebraic connectivity of directed graphs

We consider a generalization of Fiedler's notion of algebraic connectivity to directed graphs. We show that several properties of Fiedler's definition remain valid for directed graphs and present properties peculiar to directed graphs. We prove inequalities relating the algebraic connectiv...

Full description

Saved in:
Bibliographic Details
Published inLinear & multilinear algebra Vol. 53; no. 3; pp. 203 - 223
Main Author Wu, Chai Wah
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.06.2005
Subjects
AMS Mathematics Subject Classifications: 05C20
Connectivity
Directed graphs
Dynamical systems
Eigenvalues
Laplacian matrix
Synchronization
Online AccessGet full text

Cover

More Information
Summary:We consider a generalization of Fiedler's notion of algebraic connectivity to directed graphs. We show that several properties of Fiedler's definition remain valid for directed graphs and present properties peculiar to directed graphs. We prove inequalities relating the algebraic connectivity to quantities such as the bisection width, maximum directed cut and the isoperimetric number. Finally, we illustrate an application to the synchronization in networks of coupled chaotic systems.
ISSN:0308-1087
1563-5139
DOI:10.1080/03081080500054810