R/GoogleMatrix.R

In leb-fmvz-usp/epinemo: An R Package for EPIdemiological NEtwork MOdels

#' This function creates the Google Matrix
#' @description A function to calculate the Google Matrix.
#' @param A network adjacency \code{\link{matrix}} 
#' @param alpha scaling parameter in PageRank model. It must be \code{\link{numeric}} between 0 and 1 inclusive. Default = 0.85.
#' @return Google \code{\link{matrix}}.
#' @details This function calculates the Google Matrix [2].
#' 
#' @references 
#' [1] Page L, Brin S, Motwani R, Winograd T (1999). "The PageRank 
#' Citation Ranking: Bringing Order to the Web." Stanford Digital 
#' Library Technologies Project 1999.
#' \url{http://ilpubs.stanford.edu:8090/422/1/1999-66.pdf}
#' 
#' [2] Langville AN, Meyer CD (2006). "Google's PageRank and Beyond: The Science 
#' of Search Engine Rankings." Princeton University Press, Princeton.
#' 
#' @export
#' @examples 
#' # Generate an arbitrary 100 by 100 adjacency matrix with zeros and ones
#' # Remove loops
#' A <- matrix(rbinom(100 * 100, 1, 0.2), ncol = 100, nrow = 100)
#' diag(A) <- 0
#' 
#' # Calculates Google Matrix
#' GoogleMatrix(A)

GoogleMatrix <- function(A,alpha=0.85)
{
  Srow <- rowSums(A)
  n  <- dim(A)[1]
  G <- matrix(0,n,n)
  for (i in 1:n)
  {
    if (Srow[i] != 0)
      G[i,] <- alpha*(A[i,]/Srow[i]) + (1/n)*(1-alpha)
    else
      G[i,] <- 1/n
  }
  return(G)
}