sp_eigen_adj: Eigen decomposition of matrices associated with graphs
In baruuum/btoolbox: random toolbox

Description Usage Arguments Details Value

Eigen decomposition of matrices associated with graphs

sp_eigen_adj(
  x,
  k,
  type = c("adj", "adj_sym", "adj_left", "lap", "lap_sym", "lap_left"),
  check = c("all", "symmetric", "isolates", "none"),
  set_diag_zero = FALSE
)

`x`	adjacency matrix (or affiliation matrix) of a graph; must be a `Matrix::sparseMatrix` and symmetric
`k`	number of eigenparis to extract (largest algebraic values for adjacency matrix and smallest algebraic values for Laplacian matrix)
`type`	string that is either `"adj", "adj_sym", "adj_left", "lap", "lap_sym", "lap_left"`, standing for, respectively, the adjacency matrix (`x`), the normalized (symmetric) adjacency matrix, the (left) normalized adjacency matrix, the Laplacian, the normalized (symmetric) Laplacian, or the (left) normalized Laplacian.
`check`	string of ether "all" (default), "isolates," "symmetric," or "none." Checks whether there are dangling nodes or whether `x` is asymmetric (or both/none), and throws error if so
`set_diag_zero`	if `TRUE`, the diagonals of `x` are set to zero before computing decomposition

Let A be the adjacency matrix associated with graph G. The Laplacian is given as

L = D - A

, where D is a diagonal matrix containing the degrees. Let I be the identity matrix of same dimensions as A. Then the different versions of normalized adjacency and Laplacian matrices are defined as follows:

Normalized (symmetric) adjacency matrix:

A_{s} = D^{-1/2}AD^{-1/2}

(Left) normalized adjacency matrix:

A_{l} = D^{-1}A

Normalized (symmetric) Laplacian:

L_{s} = I - A_{s}

(Left) normalized Laplacian:

L_{l} = I - A_{l}

returns the k largest/smallest eigenpairs of the requested matrix. Eigenvalues, and their corresponding eigenvectors, are ordered in decreasing order for adjacency matrices and in increasing order for Laplacian matrices.

baruuum/btoolbox documentation built on Aug. 17, 2020, 1:29 a.m.