Re #32 added centralization functions for degree, closeness, and betw…

…eenness

NAMESPACE

@@ -5,6 +5,9 @@ export(.E)
 export(.G)
 export(.N)
 export(as_incidence_matrix)
+export(centralisation_betweenness)
+export(centralisation_closeness)
+export(centralisation_degree)
 export(centrality_betweenness)
 export(centrality_closeness)
 export(centrality_degree)

R/centralization.R

@@ -0,0 +1,139 @@
+#' Centralization for one- and two-mode graphs
+#'
+#' This function allows you to calculate how (degree) centralized a two-mode graph is.
+#' @name centralization
+#' @family two-mode functions
+#' @param object A matrix, igraph graph, or tidygraph object
+#' @param modes Whether to calculate centralization for the graph as a whole (`modes = "all"`),
+#' or, if two-mode, for each nodeset (`modes = "each"`).
+#' @param ... 
+#' @return The centralization score. 
+#' If `modes = "each"`, then a named list of two scores will be returned.
+#' To return just the score for the first nodeset (rows), 
+#' append `$nodes1` to the end of the function call or returned object.
+#' To return just the score for the second nodeset (cols), 
+#' append `$nodes2` to the end of the function call or returned object.
+#' @references Borgatti, Stephen P, and Daniel S Halgin. 2011. ``Analyzing Affiliation Networks." In \emph{The SAGE Handbook of 
+#' Social Network Analysis}, edited by John Scott and Peter J Carrington, 417–33. London, UK: Sage.
+#' @examples
+#' \dontrun{
+#' centralization_degree(graph)
+#' }
+#' @export
+centralisation_degree <- centralization_degree <- function(object, 
+                                                           modes = c("all", "each"), 
+                                                           ...){
+
+  graph <- converge_to_igraph(object)
+
+  modes <- match.arg(modes)
+
+  if(modes == "all"){
+    nodeset <- names(which(igraph::degree(graph)==max(igraph::degree(graph)))) %in%
+      V(graph)$name[V(graph)$type==T]
+    m <- length(which(V(graph)$type==T))
+    n <- length(which(V(graph)$type!=T))
+
+    out <- sum(max(igraph::degree(graph)[which(V(graph)$type==nodeset)], na.rm=T)-
+          igraph::degree(graph)[which(V(graph)$type==nodeset)])/((n-1)*(m-1))
+  } else if (modes == "each"){
+    out <- vector()
+    out$nodes1 <- "score1"
+    out$nodes2 <- "score2"
+  } else stop("Mode not recognised")
+
+}
+
+#' @rdname centralization
+#' @family two-mode functions
+#' @export
+centralisation_closeness <- centralization_closeness <- function(object, 
+                                                                 modes = c("all", "each"), 
+                                                                 ...){
+
+  graph <- converge_to_igraph(object)
+
+  modes <- match.arg(modes)
+
+  if(modes == "all"){
+    nodeset <- names(which(igraph::closeness(graph)==max(igraph::closeness(graph)))) %in% 
+      igraph::V(graph)$name[igraph::V(graph)$type==T]
+    m <- length(which(igraph::V(graph)$type==nodeset))
+    n <- length(which(igraph::V(graph)$type!=nodeset))
+
+    if (m > n) {
+      sum(max(igraph::closeness(graph)[which(igraph::V(graph)$type==nodeset)], na.rm=T)-
+            igraph::closeness(graph)[which(igraph::V(graph)$type==nodeset)])/
+        (((n-1)*(m-1)/((2*m)-3)) + ((n-1)*(m-n)/m+n-2))
+    }
+    if (m <= n) {
+      sum(max(igraph::closeness(graph)[which(igraph::V(graph)$type==nodeset)], na.rm=T)-
+            igraph::closeness(graph)[which(igraph::V(graph)$type==nodeset)])/
+        ((m-2)*(m-1)/((2*m)-3)) 
+    }
+  } else if (modes == "each"){
+    out <- vector()
+    out$nodes1 <- "score1"
+    out$nodes2 <- "score2"
+  } else stop("Mode not recognised")
+
+}
+
+#' @rdname centralization
+#' @family two-mode functions
+#' @export
+centralisation_betweenness <- centralization_betweenness <- function(object, 
+                                                                     modes = c("all", "each"), 
+                                                                     ...){
+
+  graph <- converge_to_igraph(object)
+
+  modes <- match.arg(modes)
+
+  if(modes == "all"){
+    # Whole network centralization
+    bnorm <- c(betweenness(graph)[which(V(graph)$type!=nodeset)]/
+                 ((1/2)*(m^2*(s+1)^2+m*(s+1)*(2*t-s-1)-t*(2*s-t+3))),
+               betweenness(graph)[which(V(graph)$type==nodeset)]/
+                 ((1/2)*(n^2*(p+1)^2+n*(p+1)*(2*r-p-1)-r*(2*p-r+3))))
+    sum(max(bnorm)-bnorm)/
+      ((m+n-1) - ((p*(n-r)*(2*m+2*n-p-3) + r*(p+1)*(2*m+2*n-p-4))/
+                   (m^2*(s+1)^2+m*(s+1)*(2*t-s-1)-t*(2*s-t+3))))
+
+    #   if (m > n){
+    #     sum(max(betweenness(graph))-betweenness(graph))/
+    #       (2*(m-1)*(n-1)*(m+n-1) - (n-1)*(m+n-2) - (1/2)*(m-n)*(m+3*n-3))
+    #   }
+    #   if (m <= n){
+    #     sum(max(betweenness(graph))-betweenness(graph))/
+    #       (((1/2)*n*(n-1)+(1/2)*(m-1)*(m-2)+(m-1)*(n-2)) * ((m+n-1)+(m-1)))
+    #   }
+
+  } else if (modes == "each"){
+    nodeset <- names(which(betweenness(graph)==max(betweenness(graph)))) %in% 
+      V(graph)$name[V(graph)$type==T]
+    m <- length(which(V(graph)$type==nodeset))
+    n <- length(which(V(graph)$type!=nodeset))
+    # p <- (m-1)%/%n
+    # r <- (m-1)%%n
+    # s <- (n-1)%/%m
+    # t <- (n-1)%%m
+    # 
+    # Event side centralization
+    # sum(max(betweenness(graph)[which(V(graph)$type==nodeset)])-
+    #       betweenness(graph)[which(V(graph)$type==nodeset)])/
+    #   ((m-1)*(n^2*(p+1)^2 + n*(p+1)*(2*r-p-1)-r*(2*p-r+3)))/2
+    if (m > n){
+      sum(max(betweenness(graph)[which(V(graph)$type==nodeset)], na.rm=T)-
+            betweenness(graph)[which(V(graph)$type==nodeset)])/
+        (2*(m-1)^2*(n-1))
+    }
+    if (m <= n){
+      sum(max(betweenness(graph)[which(V(graph)$type==nodeset)], na.rm=T)-
+            betweenness(graph)[which(V(graph)$type==nodeset)])/
+        ((m-1)*((1/2)*n*(n-1)+(1/2)*(m-1)*(m-2)+(m-1)*(n-1)))
+    }
+
+  } else stop("Mode not recognised")
+
+}