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#' Gateway Coefficient
#' @description Computes the gateway coefficient for each node. The gateway
#' coefficient measures a node's connections between its community and other communities.
#' Nodes that are solely responsible for inter-community connectivity will
#' have higher gateway coefficient values. Positive and negative signed weights
#' for gateway coefficients are computed separately.
#'
#' @param A Network adjacency matrix
#'
#' @param comm A vector of corresponding to each item's community.
#' Defaults to \code{"walktrap"} for the \code{\link[igraph]{cluster_walktrap}} community detection algorithm.
#' Set to \code{"louvain"} for the \code{\link[NetworkToolbox]{louvain}} community detection algorithm.
#' Can also be set to user-specified communities (see examples)
#'
#' @param cent Centrality to community gateway coefficient.
#' Defaults to \code{"strength"}.
#' Set to \code{"betweenness"} to use the \code{\link[NetworkToolbox]{betweenness}} centrality
#'
#' @return Returns a list containing:
#'
#' \item{overall}{Gateway coefficient without signs considered}
#'
#' \item{positive}{Gateway coefficient with only positive sign}
#'
#' \item{negative}{Gateway coefficient with only negative sign}
#'
#' @examples
#' #theoretical communities
#' comm <- rep(1:8, each = 6)
#'
#' # Pearson's correlation only for CRAN checks
#' A <- TMFG(neoOpen, normal = FALSE)$A
#'
#' gw <- gateway(A, comm = comm)
#'
#' #walktrap communities
#' wgw <- gateway(A, comm = "walktrap")
#'
#' @references
#' Rubinov, M., & Sporns, O. (2010).
#' Complex network measures of brain connectivity: Uses and interpretations.
#' \emph{NeuroImage}, \emph{52}, 1059-1069.
#'
#' Vargas, E. R., & Wahl, L. M. (2014).
#' The gateway coefficient: A novel metric for identifying critical connections in modular networks.
#' \emph{The European Physical Journal B}, \emph{87}, 1-10.
#'
#' @author Alexander Christensen <alexpaulchristensen@gmail.com>
#'
#' @export
#Gateway Coefficient----
gateway <- function (A, comm = c("walktrap","louvain"),
cent = c("strength","betweenness"))
{
#make sure its a matrix
A <- as.matrix(A)
#nodes
n <- ncol(A)
#set diagonal to zero
diag(A) <- 0
#set communities
if(missing(comm))
{comm<-"walktrap"
}else{comm<-comm}
#check if comm is character
if(is.character(comm))
{
if(length(comm) == 1)
{
facts <- switch(comm,
walktrap = suppressWarnings(igraph::walktrap.community(convert2igraph(A))$membership),
louvain = suppressWarnings(louvain(A)$community)
)
}else{
uni <- unique(comm)
facts <- comm
for(i in 1:length(uni))
{facts[which(facts==uni[i])] <- i}
}
}else{facts <- comm}
if(missing(cent))
{cent<-"strength"
}else{cent<-match.arg(cent)}
gate <- function (W, t)
{
S <- colSums(W)
Gc <- (W!=0)%*%diag(facts)
Sc2 <- vector(mode="numeric",length=n)
ksm <- vector(mode="numeric",length=n)
centm <- vector(mode="numeric",length=n)
if(t=="strength")
{cents <- as.vector(S)
}else if(t=="betweenness")
{cents <- as.vector(as.matrix(betweenness(W)))}
for(i in 1:max(facts))
{
ks <- rowSums(W*(Gc==i))
Sc2 <- Sc2 + (ks^2)
for(j in 1:max(facts))
{
ksm[facts==j] <- ksm[facts==j] + (ks[facts==j]/(sum(ks[facts==j])))
}
centm[facts==i] <- sum(cents[facts==i])
}
centm <- centm/max(centm)
gs <- (1-(ksm*centm))^2
GW <- (vector(mode="numeric",n)+1) - (Sc2/(S^2)*gs)
GW[is.na(GW)]<-0
GW[!GW]<-0
return(GW)
}
GWpos <- gate(W=ifelse(A>0,A,0),t=cent)
GWneg <- gate(W=ifelse(A<0,A,0),t=cent)
GW <- gate(W=A,t=cent)
return(list(overall=GW,positive=GWpos,negative=GWneg))
}
#----
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