A note on Fiedler vectors interpreted as graph realizations

Operations Research Letters

Volumn 38, Issue 4, 2010, Pages 320-321

  Helmberg, Christoph ^a   Reiss, Susanna ^a  

^a CHEMNITZ UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Eigenvalue optimization; Embedding; Graph partitioning; Semidefinite programming; Spectral graph theory

Indexed keywords

AS GRAPH; EIGEN-VALUE; EIGENSPACES; EIGENVALUE OPTIMIZATION; EIGENVECTORS; FIEDLER VECTORS; GEOMETRIC INTERPRETATION; GRAPH PARTITIONING; LAPLACE MATRIX; LAPLACIANS; OPTIMAL SOLUTIONS; REALIZATION PROBLEMS; SEMI-DEFINITE PROGRAMMING; SMALLEST EIGENVALUE; SPECTRAL GRAPH PARTITIONING; SPECTRAL GRAPH THEORY; STRUCTURAL INFORMATION;

GRAPH THEORY; LAPLACE TRANSFORMS; MATHEMATICAL PROGRAMMING; PROGRAM INTERPRETERS;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 77955307726     PISSN: 01676377     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.orl.2010.01.005     Document Type: Article

References (12)

1. T. Biyikoglu, J. Leydold, and P.F. Stadler Laplacian Eigenvectors of Graphs Lecture Notes in Mathematics vol. 1915 2007 Springer Berlin Heidelberg
2. D. Cvetkovi, M. Doob, and H. Sachs Spectra of Graphs. Theory and Application 3rd edition 1995 J. A. Barth Verlag Leipzig
3. M. Fiedler Algebraic connectivity of graphs Czechoslovak Mathematical Journal 23 1973 298 305
4. M. Fiedler A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory Czechoslovak Mathematical Journal 25 1975 619 633
5. M. Fiedler Laplacian of graphs and algebraic connectivity Combinatorics and Graph Theory 25 1989 57 70
6. M. Fiedler Absolute algebraic connectivity of trees Linear and Multilinear Algebra 26 1990 85 106
7. F. Göring, C. Helmberg, S. Reiss, Graph realizations associated with minimizing the maximum eigenvalue of the Laplacian, Preprint 2009-10, Fakultät für Mathematik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany, May 2009 (submitted for publication).
8. F. Gring, C. Helmberg, and M. Wappler Embedded in the shadow of the separator SIAM Journal on Optimization 19 1 2008 472 501
9. F. Göring, C. Helmberg, M. Wappler, The rotational dimension of a graph. Preprint 2008-16, Fakultät für Mathematik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany, Oct. 2008, Journal of Graph Theory (in press).
10. B. Mohar Graph Laplacians L.W. Beineke, R.J. Wilson, Topics in Algebraic Graph Theory Encyclopedia of Mathematics and its Applications vol. 102 2004 Cambridge University Press 113 136
11. J. Sun, S. Boyd, L. Xiao, and P. Diaconis The fastest mixing Markov process on a graph and a connection to a maximum variance unfolding problem SIAM Review 48 4 2006 681 699
12. U. von Luxburg, M. Belkin, and O. Bousquet Consistency of spectral clustering The Annals of Statistics 36 2 2008 555 586