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 language | English |
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Title of host publication | Proceedings - 11th International Conference on Signal Image Technology and Internet Based Systems |
Subtitle of host publication | SITIS 2015 |
Editors | Kokou Yetongnon, Albert Dipanda, Richard Chbeir |
Place of Publication | Los Alamitos, CA |
Publisher | IEEE |
Pages | 358-365 |
Number of pages | 8 |
ISBN (Electronic) | 978-1-4673-9721-6 |
DOIs | |
Publication status | Published - 23 Nov 2015 |
Event | 11th International Conference on Signal-Image Technology and Internet-Based Systems (SITIS) - Bangkok, Thailand Duration: 23 Nov 2015 → 27 Nov 2015 Conference number: 11 http://www.sitis-conf.org/past-conferences/www.sitis-conf.org-2015/index.php.html |
Conference
Conference | 11th International Conference on Signal-Image Technology and Internet-Based Systems (SITIS) |
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Abbreviated title | SITIS 2015 |
Country/Territory | Thailand |
City | Bangkok |
Period | 23/11/15 → 27/11/15 |
Internet address |
Keywords
- Gaussian distribution
- Complex networks
- graph spectral
- Eigenvector matrix