Spectral layout
In today's article, we are going to further explore Spectral layout, a topic that has been the subject of interest and debate for a long time. Spectral layout is a topic that covers a wide variety of aspects, from its historical origins to its relevance in contemporary society. Over the years, Spectral layout has sparked interest from professionals, academics, and enthusiasts alike, leading to numerous debates and research surrounding this topic. In this article, we are going to analyze different aspects of Spectral layout, examining its impact, implications, and evolution over time. In addition, we will also explore the different perspectives and opinions that exist around Spectral layout, with the aim of providing a global and complete vision on this topic. Get ready to enter the fascinating world of Spectral layout!
Spectral layout is a class of algorithm for drawing graphs. The layout uses the eigenvectors of a matrix, such as the Laplace matrix of the graph, as Cartesian coordinates of the graph's vertices.
The idea of the layout is to compute the two largest (or smallest) eigenvalues and corresponding eigenvectors of the Laplacian matrix of the graph and then use those for actually placing the nodes. Usually nodes are placed in the 2 dimensional plane. An embedding into more dimensions can be found by using more eigenvectors. In the 2-dimensional case, for a given node which corresponds to the row/column in the (symmetric) Laplacian matrix of the graph, the and -coordinates are the -th entries of the first and second eigenvectors of , respectively.
References
- Beckman, Brian (1994), Theory of Spectral Graph Layout, Tech. Report MSR-TR-94-04, Microsoft Research.
- Koren, Yehuda (2005), "Drawing graphs by eigenvectors: theory and practice", Computers & Mathematics with Applications, 49 (11–12): 1867–1888, doi:10.1016/j.camwa.2004.08.015, MR 2154691.
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