Using ARPACK to compute the largest eigenvalue of a matrix

Thanks to Gábor Csárdi, author of the R interface to ARPACK, for this example of using (the R/Igraph interface to) arpack for finding the largest eigenvalue of a matrix. The key insight is that arpack solves the function passed to it; it is this nature of this function which determines if arpack returns eigenvalues or the graph laplacian or etc. Note that the adjacency matrix gets passed to arpack via this function, so there is some dependence on scoping (arpack has an option to specify the environment, so encapsulation is possible if desired).

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require(Matrix) ## for sparse matrices
require(igraph) ## for the function arpack
 
## assume you already have an igraph object, though any (sparse) matrix object should work
mymat <- get.adjacency(mygraph,sparse=TRUE)
func <- function(x, extra=NULL) { as.vector(mymat %*% x) } 
vals <- arpack(func, options=list(n=vcount(mygraph), nev=3, ncv=8, sym=TRUE,
                                  which="LM", maxiter=200))$values

file under “completing the function documentation”