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#' Average Path Length
#'
#' @description Calculate the average path length of a graph.
#' @param Network The input network.
#' @param probability The confidence level probability.
#' @param error The sampling error.
#' @param Cores Number of cores to use in the computations. By default uses \emph{parallel} function \code{detecCores()}.
#' @param full.apl It will calculate the sampling version by default. If it is set to true,
#' the population APL will be calculated and the rest of the parameters will be ignored.
#' @details The average path length (APL) is the average shortest path lengths of all
#' pairs of nodes in graph \emph{Network}. \code{metric.distance.apl} calculates
#' the population APL and estimated APL of graph g with a sampling error set by the user.
#'
#' The calculation uses a parallel load balancing approach,
#' distributing jobs equally among the cores defined by the user.
#' @return A real value.
#' @author Luis Castro, Nazrul Shaikh.
#' @examples \dontrun{
#' ##Default function
#' x <- net.erdos.renyi.gnp(1000,0.01)
#' metric.distance.apl(x)
#' ##Population APL
#' metric.distance.apl(x, full.apl=TRUE)
#' ##Sampling at 99% level with an error of 10% using 5 cores
#' metric.distance.apl(Network = x, probability=0.99, error=0.1, Cores=5)
#'}
#'
#' @import parallel
#' @import doParallel
#' @import foreach
#' @export
#' @references E. W. Dijkstra. 1959. A note on two problems in connexion with graphs. Numer. Math. 1, 1 (December 1959), 269-271.
#' @references Castro L, Shaikh N. Estimation of Average Path Lengths
#' of Social Networks via Random Node Pair Sampling.
#' Department of Industrial Engineering, University of Miami. 2016.
metric.distance.apl <- function(Network,probability=0.95,error=0.03,
Cores=detectCores(), full.apl=FALSE){
if (!is.list(Network)) stop("Parameter 'Network' must be a list", call. = FALSE)
if (probability>=1 | probability<=0) stop("Parameter 'probability' must be in (0,1)", call. = FALSE)
if (error>1 | error<0) stop("Parameter 'error' must be in [0,1]", call. = FALSE)
if (Cores <= 0 | Cores%%1!=0) stop("Parameter 'Cores' must be a positive integer number",call. = FALSE)
if (Cores > detectCores()) stop("Parameter 'Cores' exceeds the max number of available cores",call. = FALSE)
if (!is.logical(full.apl)) stop("Parameter 'full.ap' must be logical", call. = FALSE)
if (0 %in% lengths(Network)) stop("The network object contains isolated nodes", call = FALSE)
##//Inner function SPL by edeges
Shortest.path.big <- function(matrix.edges,network){
##Parameters
#matrix.edges <- edges by rows, first element source, second element destination - for apply use!!
#network in list representation
Shortest.path.int <- function(edge,Network){
##//Parameters
#orig - source node
#dest - final destination node
#Network - egocentric representation of the network
##Computation
sp <- 1
r1 <- 0
#edge <- unlist(edge)
orig <- edge[1]
dest <- edge[2]
##Correcting same origen and destination
if (orig==dest){
#print("Si")
x <- setdiff(seq(length(Network)),orig)
#print(length(x))
dest <- sample(x,1)
#print(dest)
}
##Loop of SP
while (r1==0){
if (sp==1){
neig <- unlist(Network[orig])
r1 <- which(neig==dest)
r1 <- length(r1)
}
if (r1==0){
neig <- unique(unlist(Network[neig]))
r1 <- which(neig==dest)
r1 <- length(r1)
sp <- sp+1
}
}
sp
}
output <- apply(matrix.edges,1,Shortest.path.int,Network=network)
output
}
##//Sample nodes
set.seed(0)
#Get 1000 of SP for st dev calculation for sampling
N <- length(Network)
s <- round(1000/Cores)*Cores
x <- array(seq(N))
S1 <- matrix(nrow=s,ncol=2)
s1 <- sample(x,s,replace=TRUE); S1[,1] <- s1
s1 <- sample(x,s,replace=TRUE); S1[,2] <- s1
s1 <- c(seq(1,length(s1),length(s1)/Cores),length(s1)+1)
S <- list()
for (i in 1:(length(s1)-1)){
S[[i]] <- S1[s1[i]:(s1[i+1]-1),]
}
cl <- makeCluster(Cores)
on.exit(stopCluster(cl))
registerDoParallel(cl, cores = Cores)
v <- parLapply(cl=cl,S,Shortest.path.big,network=Network)
v <- stats::sd(unlist(v))
#Final sample size
#/Sample APL
if (full.apl==FALSE){
d <- 1-probability
Z <- stats::qnorm(1-d/2)
s <- round((min(N,(Z*v/error)**2)/Cores))*Cores
S1 <- matrix(nrow=s,ncol=2)
s1 <- sample(x,s,replace=TRUE); S1[,1] <- s1
s1 <- sample(x,s,replace=TRUE); S1[,2] <- s1
s1 <- c(seq(1,length(s1),length(s1)/Cores),length(s1)+1)
S <- list()
for (i in 1:(length(s1)-1)){
S[[i]] <- S1[s1[i]:(s1[i+1]-1),]
}
}
#/Full APL
if (full.apl==TRUE){
s <- floor(N/Cores)*Cores
S1 <- matrix(nrow=s,ncol=2)
s1 <- sample(x,s,replace=FALSE); S1[,1] <- s1
s1 <- sample(x,s,replace=FALSE); S1[,2] <- s1
s1 <- c(seq(1,length(s1),length(s1)/Cores),length(s1)+1)
S <- list()
for (i in 1:(length(s1)-1)){
S[[i]] <- S1[s1[i]:(s1[i+1]-1),]
}
}
##/Parallel processing
#cl <- makeCluster(Cores)
#on.exit(stopCluster(cl))
registerDoParallel(cl, cores = Cores)
Paths <- parLapply(cl=cl,S,Shortest.path.big,network=Network)
return(mean(unlist(Paths)))
}
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