#This code operationalizes Everett's and Borgatti's (2005) equation 4.10 for two centralization. Code written by Jesse Sayles, 24 Feb 2015

#Citation:  Everett M, Borgatti SP (2005) Extending centrality. Models and Methods in Social Network Analysis, eds Carrington P, Scott J, Wasserman S (Cambridge Univ Press, Cambridge, UK), pp 57-76. 

#The code takes a two mode network and calculates centralization. The code can handle isolates in the graph and will remove these before calculating centralization. So, centralization is calculated on a graph with no isolates. 

#create function for Everett and Borgatti (2005) equation 4.10
EverettBorgatti2modeCent<-function(twomode){ 
    dcM1<-subset(rowSums(twomode),rowSums(twomode)>0)
    dcM2<-subset(colSums(twomode),colSums(twomode)>0)
    normM1<-dcM1/length(dcM2)
    normM2<-dcM2/length(dcM1)
    allNodesNorm<-c(normM1,normM2)
    if(max(dcM1)==max(max(dcM1),max(dcM2))){No<-length(dcM1);Ni<-length(dcM2)}else{No<-length(dcM2);Ni<-length(dcM1)}
    return ((sum(max(allNodesNorm)-allNodesNorm)) / (((((No*Ni)-Ni-No+1))*(Ni+No)) / (Ni*No))) }
  
    
#this should come out to centralization = 1
test1<-matrix(c(
       1,1,1,1,1,
       1,0,0,0,0,
       1,0,0,0,0,
       1,0,0,0,0,
       1,0,0,0,0),nrow=5,ncol=5,byrow=T)
     
EverettBorgatti2modeCent(test1)
  

#this should also come out to centralization = 1 b/c we remove isos
test2<-matrix(c(
       1,1,0,1,1,
       1,0,0,0,0,
       0,0,0,0,0,
       1,0,0,0,0,
       1,0,0,0,0),nrow=5,ncol=5,byrow=T)

EverettBorgatti2modeCent(test2)


#this should  come out to centralization = 0
test3<-matrix(c(
       1,1,1,1,1,
       1,1,1,1,1,
       1,1,1,1,1,
       1,1,1,1,1,
       1,1,1,1,1),nrow=5,ncol=5,byrow=T)

EverettBorgatti2modeCent(test3)


#this should come out to centralization = NA b/c we divide by zero which we must interpret as centralization = 1
test4<-matrix(c(
       1,1,1,1,1),nrow=1,ncol=5,byrow=T)
      
EverettBorgatti2modeCent(test4)