%%% Random Graphs
clc
clf
format compact
format short g
% Fixes the Random Number System
% Comment out the next line to change the output
%rand('state',357) 
N=150;
x=rand(1,N);
y=rand(1,N);
plot(x,y,'x')
xmatrix = x'*ones(1,N);
xdist = abs(xmatrix-xmatrix');
ymatrix = y'*ones(1,N);
ydist = abs(ymatrix-ymatrix');
dist = sqrt(xdist.^2+ydist.^2);
R=0.1
B = (dist<R)-eye(N);
%hold on
%for jj=1:N-1
%    for jjj=[jj+1:N]
%        if B(jj,jjj)==1
%            plot(x([jj jjj]), y([jj jjj]))
%        end
%    end
%end
%hold off
%K=.1/max(eig(B));
%B1=K*B;
%C = (B1-B1^N)/(eye(N)-B1);
%sum(C>0)';
%max(ans)

N=200
blocks=floor(sqrt(N)/2)
M=round(2*rand(1,N)+0.5);
y = (round(blocks*rand(1,N)+.5)-.5)/blocks
x = rand(1,N);
for k=1:N
    if M(k) ==2
        dummy=x(k);
        x(k)=y(k);
        y(k) = dummy;
    end
end
plot(x,y,'x')
xmatrix = x'*ones(1,N);
xdist = abs(xmatrix-xmatrix');
ymatrix = y'*ones(1,N);
ydist = abs(ymatrix-ymatrix');
dist = sqrt(xdist.^2+ydist.^2);
R=0.1
B = (dist<R)-eye(N);
hold on
for jj=1:N-1
    for jjj=[jj+1:N]
        if B(jj,jjj)==1
            plot(x([jj jjj]), y([jj jjj]))
        end
    end
end
hold off
K=.1/max(eig(B));
B1=K*B;
C = (B1-B1^N)/(eye(N)-B1);
sum(C>0)';
max(ans)
ans/N*100