betweenness_bin.m

function BC=betweenness_bin(G)
%BETWEENNESS_BIN    Node betweenness centrality
%
%   BC = betweenness_bin(A);
%
%   Node betweenness centrality is the fraction of all shortest paths in 
%   the network that contain a given node. Nodes with high values of 
%   betweenness centrality participate in a large number of shortest paths.
%
%   Input:      A,      binary (directed/undirected) connection matrix.
%
%   Output:     BC,     node betweenness centrality vector.
%
%   Note: Betweenness centrality may be normalised to the range [0,1] as
%   BC/[(N-1)(N-2)], where N is the number of nodes in the network.
%
%   Reference: Kintali (2008) arXiv:0809.1906v2 [cs.DS]
%              (generalization to directed and disconnected graphs)
%
%
%   Mika Rubinov, UNSW/U Cambridge, 2007-2012


n=length(G);                %number of nodes
I=eye(n)~=0;                %logical identity matrix
d=1;                     	%path length
NPd=G;                      %number of paths of length |d|
NSPd=NPd;                  	%number of shortest paths of length |d|
NSP=NSPd; NSP(I)=1;        	%number of shortest paths of any length
L=NSPd; L(I)=1;           	%length of shortest paths

%calculate NSP and L
while find(NSPd,1)
    d=d+1;
    NPd=NPd*G;
    NSPd=NPd.*(L==0);
    NSP=NSP+NSPd;
    L=L+d.*(NSPd~=0);
end
L(~L)=inf; L(I)=0;          %L for disconnected vertices is inf
NSP(~NSP)=1;                %NSP for disconnected vertices is 1

Gt=G.';
DP=zeros(n);            	%vertex on vertex dependency
diam=d-1;                  	%graph diameter

%calculate DP
for d=diam:-1:2
    DPd1=(((L==d).*(1+DP)./NSP)*Gt).*((L==(d-1)).*NSP);
    DP=DP + DPd1;           %DPd1: dependencies on vertices |d-1| from source
end

BC=sum(DP,1);               %compute betweenness