R/distance.index.R

In netrankr: Analyzing Partial Rankings in Networks

#' @title Distance-based centrality indices
#' @description Implements a variety of centrality indices that are based on geodesic distances.
#' @param g An igraph object
#' @param type character specifying the used index. See details for possibilities
#' @param alpha numeric value for parametrized indices. See details
#' @return Numeric vector with scores of the specified index
#' @author David Schoch
#' @details The \emph{type} parameter can be set to
#' \describe{
#' \item{ros}{'reciprocal of sum'. \deqn{c(u)=\frac{1}{\sum_{t \in V} dist(i,t)}}}
#' \item{sor}{'sum of reciprocals'. \deqn{c(u)=\sum_{t \in V} \frac{1}{dist(i,t)}}}
#' \item{dpow}{'distance to the power of'. \deqn{c(u)=\sum_{t \in V} dist(i,t)^{-\alpha} \quad \alpha\geq 0}}
#' \item{powd}{'to the power of distance'. \deqn{c(u)=\sum_{t \in V} \alpha^{-dist(i,t)} \quad \alpha \in (0,1)}}
#' \item{int}{'integration'. \deqn{c(u)=\sum_{t \in V} 1-\frac{dist(i,t)-1}{diameter(G)}}}
#' \item{pow2}{'distance to the power of 2'. \deqn{c(u)=\sum_{t \in V} 2^{-dist(i,t)}}}
#' }
#' @examples
#' library(igraph)
#' g <- sample_gnp(100, 0.1)
#' d_ros <- distance_index(g, type = "ros")
#' d_sor <- distance_index(g, type = "sor")
#' compare_ranks(d_ros, d_sor) # compare rankings
#' @export
# distance_index <- function(g,type='ros',alpha=1){ D <- igraph::distances(g) diam <- igraph::diameter(g) switch(type, ros={1/rowSums(D)},
# sor={R=1/D diag(R)=0 rowSums(R)}, dpow={R=(D^-alpha) diag(R)=0 rowSums(R)}, powd={rowSums(alpha^D)}, int={rowSums(1-(D-1)/diam)},
# pow2={rowSums(2^-D)} ) }