Spectral layout is a class of

algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...

for drawing graphs. The layout uses the

eigenvectors In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted ...

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

i

in the (symmetric) Laplacian matrix

L

of the graph, the

x

and

y

-coordinates are the

i

-th entries of the first and second eigenvectors of

L

, respectively.

References

*. *. Graph algorithms Graph drawing {{Mathapplied-stub