Spectral layout
Graph drawing using eigenvector coordinates
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 
Sources and credits
This article is adapted from the Wikipedia article “Spectral layout”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.
Images, from Wikimedia Commons:
- Spectral graph drawing of small world graph.svg by Apoptheosis, CC0
- Spring graph drawing of small world graph.svg by Apoptheosis, CC0
Fathomly is not affiliated with or endorsed by the Wikimedia Foundation. Spotted a problem? Tell us.