Orthogonal Eigenvector Matrix of the Laplacian

Xiangrong Wang, Piet Van Mieghem

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

2 Citations (Scopus)

Abstract

The orthogonal eigenvector matrix Z of the Laplacian matrix of a graph with N nodes is studied rather than its companion X of the adjacency matrix, because for the Laplacian matrix, the eigenvector matrix Z corresponds to the adjacency companion X of a regular graph, whose properties are easier. In particular, the column sum vector of Z (which we call the fundamental weight vector w) is, for a connected graph, proportional to the basic vector eN = (0, 0, . . . , 1), so that more information about the speclics of the graph is contained in the row sum of Z (which we call the dual fundamental weight vector φ). Since little is known about Z (or X), we have tried to understand simple properties of Z such as the number of zeros, the sum of elements, the maximum and minimum element and properties of φ. For the particular class of Erdos-Rényi random graphs, we found that a product of a Gaussian and a super-Gaussian distribution approximates accurately the distribution of ΦU, a uniformly at random chosen component of the dual fundamental weight vector of Z.
Original languageEnglish
Title of host publicationProceedings - 11th International Conference on Signal Image Technology and Internet Based Systems
Subtitle of host publicationSITIS 2015
EditorsKokou Yetongnon, Albert Dipanda, Richard Chbeir
Place of PublicationLos Alamitos, CA
PublisherIEEE
Pages358-365
Number of pages8
ISBN (Electronic)978-1-4673-9721-6
DOIs
Publication statusPublished - 23 Nov 2015
Event11th International Conference on Signal-Image Technology and Internet-Based Systems (SITIS) - Bangkok, Thailand
Duration: 23 Nov 201527 Nov 2015
Conference number: 11
http://www.sitis-conf.org/past-conferences/www.sitis-conf.org-2015/index.php.html

Conference

Conference11th International Conference on Signal-Image Technology and Internet-Based Systems (SITIS)
Abbreviated titleSITIS 2015
Country/TerritoryThailand
CityBangkok
Period23/11/1527/11/15
Internet address

Keywords

  • Gaussian distribution
  • Complex networks
  • graph spectral
  • Eigenvector matrix

Fingerprint

Dive into the research topics of 'Orthogonal Eigenvector Matrix of the Laplacian'. Together they form a unique fingerprint.

Cite this