spectral_coords {gasper}

Spectral Coordinates for Graph Drawing

Description

Calculates the spectral coordinates of a graph using the two smallest non-zero eigenvalues of the graph Laplacian.

Usage

spectral_coords(adj_mat)

Arguments

adj_mat

A symmetric adjacency matrix or sparse matrix representing an undirected graph.

Details

The spectral_coords function implements a 2-dimensional spectral graph drawing method based on the eigenvectors of the graph Laplacian associated with its two smallest non-zero eigenvalues. Given a graph with adjacency matrix adj_mat, the graph Laplacian L is computed, which is a matrix representation that encodes the graph's topology. The Laplacian's eigenvalues and eigenvectors are calculated, and the eigenvectors corresponding to the second and third non-zero smallest eigenvalues are used to determine the coordinates of the graph's vertices in the plane.

Value

A matrix where each row represents the spectral coordinates of a node in the graph.

References

Chung, F. R. K. (1997). Spectral Graph Theory. American Mathematical Soc.

Hall, K. M. (1970). An r-dimensional quadratic placement algorithm. Management science, 17(3), 219-229.

See Also

plot_graph, plot_signal

Examples

## Not run: 
matrixname <- "bcspwr02"
groupname <- "HB"
download_graph(matrixname,groupname)
xy <- spectral_coords(bcspwr02$sA)
bcspwr02$xy <- xy
plot_graph(bcspwr02)

## End(Not run)