%This function creates the google matrix and probability vector for a
%network.

function [GMatrix,BiggestEigenvector]=GMatrixMaker(AMatrix,q)

%This part creates the Google matrix

n=length(AMatrix);                  %Amount of elements in network
G1=(q/n).*ones(n,n);                %First part of google equation formula
G3=sum(AMatrix').^-1;               %Last part of google equation
G3=repmat(G3,n,1);                  %Making last part correct size
G2=(AMatrix.').*((1-q).*G3);        %Middle part of google matrix
GMatrix=G1+G2;                      %Creating the google matrix

%This part finds the eigenvector corresponding to the biggest eigenvalue

[EigenVectors,EigenValues]=eig(GMatrix);
[BiggestEigenvalue,BiggestEigenvaluePosition]=max(max(EigenValues));
BiggestEigenvector=EigenVectors(:,BiggestEigenvaluePosition);
BiggestEigenvector=BiggestEigenvector/sum(BiggestEigenvector);