surprise.m

function [S] = surprise(A, ci, base10)
%SURPRISE      Compute surprise of a vertex partition on a binary network.
%
%
%   Inputs      A,  undirected binary network. If weighted, weights are
%                   ignored.
%               ci, membership vector
%				base10, if nonzero use base10 logarithms
%
%   Outputs:    S,  value of Surprise (is log10 base, to get natural logarithm,
%                   multiply S by log(10)).
%
%   Carlo Nicolini, Istituto Italiano di Tecnologia (2016).
%
if nargin==2
	base10=true;
end
if length(unique(A(:))) ~= 2
    warning on;
    warning('Input matrix is not binary {0,1}. Ignoring edge weights to compute Surprise.');
end

% Get the block matrix
[B,C,~,~,L,M]=comm_mat(A,ci);

nc = sum(C,2); % number of nodes per community

Lin = sum(diag(B)); % number of intracluster edges
Min = sum(nc.*(nc-1)/2); % number of intracluster pairs
[Lin,L,Min,M]
S=compute_surprise(M, Min, L, Lin, base10);

% Compute the binomial surprise
-arrayfun(@(i)(logC(i,L)+i*log(Min/M)+(L-i)*(log(1-Min/M))),Lin)
L*KL(Lin/L, Min/M)