R/leverage.R

In centiserve: Find Graph Centrality Indices

#' Find the leverage centrality
#'
#' Leverage centrality considers the degree of a node relative to its neighbors and operates under the principle that a node in a network is central if its immediate neighbors rely on that node for information.
#' @details 
#' Leverage centrality of vertex \eqn{i}{i} defined as:
#' \deqn{l_{i}=\frac{1}{k_{i}}\sum_{N_{i}}\frac{k_{i}-k_{j}}{k_{i}+k_{j}}}
#' where \eqn{k_{i}}{k(i)} is degree of a given node \eqn{i}{i}, \eqn{k_{j}}{k(j)} is degree of each of its neighbors and \eqn{N_{i}}{N(i)} is all neighbors. \cr
#' A node with negative leverage centrality is influenced by its neighbors, as the neighbors connect and interact with far more nodes. A node with positive leverage centrality, on the other hand, influences its neighbors since the neighbors tend to have far fewer connections. \cr
#' More detail at \href{http://www.centiserver.org/?q1=centrality&q2=Leverage_Centrality}{Leverage Centrality}
#' @param graph The input graph as igraph object
#' @param vids Vertex sequence, the vertices for which the centrality values are returned. Default is all vertices. 
#' @param mode Character constatnt, it specifies how to use the direction of the edges if a directed graph is analyzed. For 'out' only the outgoing edges are followed. For 'in' all vertices from which the source vertex is reachable in at most order steps are counted. 'all' ignores the direction of the edges. This argument is ignored for undirected graphs.
#' @param loops Logical; whether the loop edges are also counted.
#' @return A numeric vector contaning the centrality scores for the selected vertices.
#' @author Mahdi Jalili \email{m_jalili@@farabi.tums.ac.ir}
#' @references Joyce, Karen E., et al. "A new measure of centrality for brain networks." PLoS One 5.8 (2010): e12200.
#' @examples
#' g <- graph(c(1,2,2,3,3,4,4,2))
#' leverage(g)
#' @export

# Thanks to Alex Upton for the implementation
# http://igraph.wikidot.com/r-recipes

leverage <- function(graph, vids = V(graph), mode = c("all", "out", "in"), loops = TRUE){
  .cs.checkPreconditions(graph)
  vids <- .cs.as.igraph.vs(graph, vids)
  k <- degree(graph, mode=mode[1], loops=as.logical(loops))
  n <- vcount(graph)
  res <- sapply(1:n, function(v) { mean((k[v]-k[neighbors(graph, v, mode=mode[1])]) / (k[v]+k[neighbors(graph, v, mode=mode[1])])) })
  if (getIgraphOpt("add.vertex.names") && is.named(graph)) {
    names(res) <- V(graph)$name
  }  
  res[vids]
}