Spectral Bisection with Two Eigenvectors

Authors: Israel Rocha
Publication year: 2017
Publication type: Článek v odborném periodiku
Periodical: Electronic Notes in Discrete Mathematics
Bibliographic citation: ROCHA, Israel. Spectral Bisection with Two Eigenvectors. Electronic Notes in Discrete Mathematics. 2017, 61(August), 1019-1025. ISSN 1571-0653
Dostupné z: doi:10.1016/j.endm.2017.07.067
DOI: 10.1016/j.endm.2017.07.067
ID: 477278

Abstract

We show a spectral bisection algorithm which makes use of the second and third eigenvector of the Laplacian matrix. This algorithm is guaranteed to return a cut that is smaller or equal to the one returned by the classic spectral bisection. To this end, we investigate combinatorial properties of certain configurations of a graph partition. These properties, that we call organized partitions, are shown to be related to the minimality and maximality of a cut. We show that organized partitions are related to the third eigenvector of the Laplacian matrix and give bounds on the minimum cut in terms of organized partitions and eigenvalues.