how can we draw graph using adjacency matrix in matlab

Hi, every on am new to matlab i want to draw a graph using adjacency matrix of image when am tried an inbuilt function called graph i am not getting the expected output please help me to draw graph.

my input image

clc;
clear all;
close all;
X=imread('one.bmp');
imfinfo('one.bmp')
figure,imshow(X)

b = imresize(X,[100,100]);
si = size(b,1);
sj = size(b,2);
%figure;imshow(b);

% Binarization
% th = graythresh(b);
% I = im2bw(b,th);
%thinning
kl=bwmorph(~b,'thin',inf);
figure,imshow(kl)
R(:,:)=kl(:,:);
%grid size 
t1=25;
D=100;
 I=1;
U1=t1;
J=1;
U2=t1;
E=1;
t2=D/t1;
%Z=1;
for iir=1:t2
    for jjr=1:t2
 B(I:U1,J:U2)=R(I:U1,J:U2);
%  vc=sum(B(I:U1,J:U2));
%  Fd=sum(vc);
 [x,y]=find(B==1);
 CX=mean(x);
 CY=mean(y);
 CXXX(E)=CX;
 CYYY(E)=CY;
 CXX(iir,jjr)=CX;
 CYY(iir,jjr)=CY;

   T(I:U1,J:U2)=B(I:U1,J:U2);
      J=J+t1;
    U2=U2+t1;
  E=E+1;
   clear B x y 

      end

I=I+t1;
U1=U1+t1;
J=1;
  U2=t1;

end
%plot and grid
figure,imshow(R)
hold on
M10 = size(R,1);
N10 = size(R,2);

a=t1; 
b=t1;
for k = 1:a:M10
    x = [1 N10]; 
   y = [k k]; 
   plot(x,y,'Color','white');
    set(findobj('Tag','MyGrid'),'Visible','on')
end
for k = 1:b:N10 
    x = [k k]; 
    y = [1 M10];
    plot(x,y,'Color','white');
    set(findobj('Tag','MyGrid'),'Visible','on')
end

plot(CYY,CXX,'g*')
%line(CYY,CXX)
%CC=bwconncomp(CXX,4)

hold off
%node neighbourhoood analyssis
N1=t2;
for I2=1:N1
    for J2=1:N1
        %last row
       if(I2>=N1)
             W1=CXX(I2,J2);
           W2=CXX(I2-1,J2);
           W3=CYY(I2,J2);
           W4=CYY(I2-1,J2);    
           W6=[W1,W2];
           W7=[W3,W4];
           line(W7,W6);
           if(J2>=N1)
               Z=CXX(I2,J2);
           else
           if (CXX(I2,J2+1)>1)&& ((CYY(I2,J2+1)>1))
            TXX=CXX(I2,J2);
            TYY=CXX(I2,J2+1);
               TTX=CYY(I2,J2);
               TTY=CYY(I2,J2+1);

              IY=[TXX,TYY];
              IIY=[TTX,TTY];
              line(IIY,IY);
             end
             end

         else
             if(J2>=N1);
               W1=CXX(I2,J2);
             W2=CXX(I2+1,J2);
             W3=CYY(I2,J2);
             W4=CYY(I2+1,J2);    
             W6=[W1,W2];
             W7=[W3,W4];
             line(W7,W6);
             else   
                 if (CXX(I2,J2+1)>1)&& ((CYY(I2,J2+1)>1))
              TXX=CXX(I2,J2);
              TYY=CXX(I2,J2+1);
                 TTX=CYY(I2,J2);
                 TTY=CYY(I2,J2+1);

              IY=[TXX,TYY];
              IIY=[TTX,TTY];
              line(IIY,IY);

                 end
           if (CXX(I2+1,J2)>1)&& ((CYY(I2+1,J2)>1))
             W1=CXX(I2,J2);
             W2=CXX(I2+1,J2);
             W3=CYY(I2,J2);
             W4=CYY(I2+1,J2);    
             W6=[W1,W2];
             W7=[W3,W4];
             line(W7,W6);
             J2=J2+1

           end
          end
      end
      end
  end

      A=zeros(t2,t2);   
      ttt=1;
     for rt=1:t2
        for  rt1=1:t2
            if(CXX(rt,rt1)>1)
                A(rt,rt1)=ttt
            end
            ttt=ttt+1;
        end
     end

g=1;
jk=1;
um=t2-1;
um1=t2;
for iir=1:t2
    for jjr=1:t2
        if(A(iir,jjr)>=0)
            BB(jk)=0;
                       DD(g)=0;
                      FF(g)=0;
                      HH(g)=0;
        end
        if(A(iir,jjr)>=1)
          if(iir==um1)&&(jjr==1)
             GG(g)=A(iir,jjr);
            HH(g)=A(iir-1,jjr); 
            BB(jk)=A(iir,jjr+1);
            DD(g)=0;
          else
              if(iir==um1)&&(jjr>1)&&(jjr<=um)
               FF(g)=A(iir,jjr-1); 
                BB(jk)=A(iir,jjr+1);
                HH(g)=A(iir-1,jjr);
              else

                if(iir==um1)&&(jjr==um1)
                    HH(g)=A(iir-1,jjr);
                    FF(g)=A(iir,jjr-1);
                    DD(g)=0;
                    BB(jk)=0;
                else

          if(iir==1)&&(jjr==um1)
              FF(g)=A(iir,jjr-1);
              DD(g)=A(iir+1,jjr);
              BB(jk)=0;

          else
              if(iir>=1)&&(iir<=um)&&(jjr==um1)
               HH(g)=A(iir-1,jjr);
               DD(g)=A(iir+1,jjr);
              FF(g)=A(iir,jjr-1);
              BB(jk)=0;
              else
                if(iir==1)&&(jjr==1)
                  BB(jk)=A(iir,jjr+1);  
                  DD(g)=A(iir+1,jjr);
                else
                if(iir==1)&&(jjr>=1)&&(jjr<=um)  
                FF(g)=A(iir,jjr-1);    
                DD(g)=A(iir+1,jjr); 
                  BB(jk)=A(iir,jjr+1);
                else
                 if(iir>1)&&(iir<=um)&&(jjr==1)   
                  HH(g)=A(iir-1,jjr);
                  DD(g)=A(iir+1,jjr);
                  BB(jk)=A(iir,jjr+1);
                 else
                     if(iir>1)&&(iir<=um)&&(jjr>1)&&(jjr<=um) 
                         BB(jk)=A(iir,jjr+1);
                     DD(g)=A(iir+1,jjr);
                     HH(g)=A(iir-1,jjr);
                      FF(g)=A(iir,jjr-1);
                     end
                 end
                end
                end
              end
          end
                end
            end
            end
          end
      g=g+1;
      jk=jk+1;
      end

end
adj=zeros(t2*t2);
H9=size(adj);
Y=1;
for ll=1:1
        for ii=1:H9(1,1)
            for jj=1:H9(1,1)
                if (ii>=4)
                    if (jj==DD(1,Y))
                    adj(ii,jj)=1;
                end
                if (jj==FF(1,Y))
                    adj(ii,jj)=1;
                end
                if (jj==BB(1,Y))
                    adj(ii,jj)=1;
                end
                if (jj==HH(1,Y))
                    adj(ii,jj)=1;
                end
                else
                if (jj==BB(1,Y))
                    adj(ii,jj)=1;
                end
                if (jj==DD(1,Y))
                    adj(ii,jj)=1;
                end
                if (jj==FF(1,Y))
                    adj(ii,jj)=1;
                end
                if (jj==HH(1,Y))
                    adj(ii,jj)=1;
                end
                end
            end
            Y=Y+1;
        end

end

this my code i have stored my adjacency matrix in an variable adj

when am tried to draw a graph using this matrix am getting the following graph am using matlab 2016a when i tried draw a graph using the graph function am getting following result

my expected output be in this form.

please help me to draw a graph as my expected image.

Answer 1

[Tobias Johansson]

The adjacency matrix only says which nodes are connected to each other. It does not say anything about how to place the nodes. You can specify layout properties in the plot function, but they may very well not correspond to what you want ('force','circle','layered','subspace'). You can also specify X and Y coordinates.

Plot graph

G = graph(adj);
p = plot(G,'layout','force')

Use coordinates specified in X and Y

p.XData = X;
p.YData = Y;

[DEEPAK P]

AM getting the output image like this

when i plot the graph using your code

[Tobias Johansson]

What I meant was that you have to specify the X and Y coordinates. I just called them X and Y and then you have to find them yourself in your code. I had trouble finding these coordinates in your code so I assumed you could. I am not familiar with your code, but this is something along the way:

M = adj;
M(~any(M,2),:) = []; % remove zero rows
M(:,~any(M,1)) = []; % remove zero columns
X = CXX'; % transpose
Y = CYY'; % transpose
X = X(:); % x vector
Y = Y(:); % y vector
X(isnan(X)) = []; % remove Nan
Y(isnan(Y)) = [];
G = graph(M); % graph
plot(G,'k','Xdata',X,'Ydata',Y,'MarkerSize',15,'NodeLabel',{}); % plot

[DEEPAK P]

thank u Tobias Johansson, how can i rotate this plotted figure?? is it possible to apply minimum spanning tree for this plotted graph??

[Christine Tobler]

It looks like your graph already has no cycles, so the minimum spanning tree of this graph is just the graph itself.

The minimum spanning tree of a graph is independent of coordinates associated with the nodes of the graph. Are you maybe looking for something like this? https://en.wikipedia.org/wiki/Euclidean_minimum_spanning_tree