%Given square matrix a, its max eigenvalue mu=mu(a) and an
%eigenvector evec is determined. mu is calculated by Karp’s
%formula. The eigenvector evec is calculated by the
%Floyd-Warshall procedure, as the first column of b^+,
%b=a/mu(a) which has diagonal entry 1.

function[mu,evec]=maxevec(a)
[m,n]=size(a);
z=[];
for i=1:n 
    z(1,i)=0; 
end;
z(1,1)=1;
for i=2:n+1
    w=z(i-1,:);
    w=max(diag(w)*a');
    z=[z;w];
end
z1=z*diag(w.^-1);
z1 =z1(1:n,:); 
for i=1:n
    t= z1(i,:); 
    z1(i,:)= t.^(1/(n+1-i));
    mu=min(max(z1)); 
    mu =mu^-1;
    b=mu^{-1}*a;
    for i=1:n
        w=b(:,i);
        u= b(i,:);
        c=w*u;
        for j=1:n
            for k=1:n
                b(j,k)=max(c(j,k),b(j,k));
            end;
        end;
    end;
    tol=10^-10;
    for i=1:n
        if abs(b(i,i)-1) < tol
            evec=b(:,i);
                return;
        end;
    end
end
end