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)


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
Number of pages8
ISBN (Electronic)978-1-4673-9721-6
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


Conference11th International Conference on Signal-Image Technology and Internet-Based Systems (SITIS)
Abbreviated titleSITIS 2015
Internet address


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


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