How to tell whether or not 5 or more lines intersect

To the left is 4 intersections, and I am trying to control the number of line intersections in my loop. The intersections I am particularly interested are coming from the chords created from intersecting circles. I want to discard iterations that create of 5 or more line intersections. How do I do that?

n       = 50;                           % Number of circles
m       = 1000;                          % Number of points on circle
r_max   = 85;                           % Maximum circle radius
r_min   = 30;                           % Minimum circle radius
x_max   = 720;                          % Uppermost x location of circle center
y_max   = 360;                          % Uppermost y location of circle center
theta   = 0:2*pi/m:2*pi;                % Evaluated angles for circle

rad     = r_max*rand(1,n);              % Set radius array size
x_pos   = x_max*rand(1,n);              % Set x-position array size
y_pos   = y_max*rand(1,n);              % Set y-position array size

i       = 1;                            % Looping value
j       = 1;                            % Circle data pointer

while i<=n                              
    j   = i+1;
    while j<=n                          % Partnering first circle with other circles
        [xout,yout] = circcirc(x_pos(i),y_pos(i),rad(i),x_pos(j),y_pos(j),rad(j));
                      mapshow(xout,yout,'DisplayType','point','Marker','o')
        plot(line([xout(1) xout(2)],[yout(1) yout(2)]))
        axis([0 x_max 0 y_max]);
        hold on

          j   = j+1;
      end
      i   = i+1;
  end

Answer 1

[Jian Wei]

After you generate the circle centers and their radii, you can run the following code to find the indices of the iterations that create less than 5 intersections.

% find each pair of circles which intersect with each other and store the information in matrix M

M = zeros(n);
for i=1:n-1
    for j=i+1:n
        if norm([x_pos(i)-x_pos(j),y_pos(i)-y_pos(j)])<rad(i)+rad(j) && norm([x_pos(i)-x_pos(j),y_pos(i)-y_pos(j)])>abs(rad(i)-rad(j))
            M(i,j)=1;
            M(j,i)=1;
        end
    end
end

% identify the iteration index which creates less than 5 intersections

index = zeros(n,1);
for i = 1:n
    ind = find(M(:,i)~=0);
    if ~isempty(ind)
        if length(ind)>=5
            continue;
        else
            M1 = M(ind,ind);
            if length(ind)+1/2*sum(sum(M1))>=5
                continue;
            else
                index(i)=1;
            end
        end
    end
end     

idx = find(index~=0);

The indices of the iterations which create less than 5 intersections are stored in the variable idx. Iterate on idx, and you can discard iterations that create 5 or more than 5 intersections.