How can I reshape a square matrix to a rectangular matrix based on its adjacency list?

How can I reshape a square matrix to a rectangular matrix based on its adjacency list? Let's say I have the following 14x14 matrix A. If it is a graph, each node has a maximum neighbors = 6. I want to create a matrix which will be 14x6. So, each row will have maximum 6 items and the values will be the non-zero items (keeping original sequence) from the original matrix, followed by zero padding.

A =

     0    -1     0     0     0     0    -2    -2     0     0     0     0     0     2
    -1     0     0     0     0     0     0     0     2     0     0     0     2     2
     0     0     0    -1     2    -1     0     0     0     0     0     0     0    -2
     0     0    -1     0     2     0     0     0     0     0     0     0     0     0
     0     0     2     2     0     0     0     0     0     0     0     0     1     2
     0     0    -1     0     0     0    -1     0     0     2     0     0     0    -2
    -2     0     0     0     0    -1     0    -1     0     2     0     0     0     0
    -2     0     0     0     0     0    -1     0    -1     0     2     0     0     0
     0     2     0     0     0     0     0    -1     0     0     2     0    -1     0
     0     0     0     0     0     2     2     0     0     0    -1     2     0     0
     0     0     0     0     0     0     0     2     2    -1     0     2     0     0
     0     0     0     0     0     0     0     0     0     2     2     0    -1     2
     0     2     0     0     1     0     0     0    -1     0     0    -1     0     0
     2     2    -2     0     2    -2     0     0     0     0     0     2     0     0

Now it's adjacency list will be (I got it from Mathematica):

 {{2, 7, 8, 14}},
 {{1, 9, 13, 14}},
 {{4, 5, 6, 14}},
 {{3, 5}},
 {{3, 4, 13, 14}},
 {{3, 7, 10, 14}},
 {{1, 6, 8, 10}},
 {{1, 7, 9, 11}},
 {{2, 8, 11, 13}},
 {{6, 7, 11, 12}},
 {{8, 9, 10, 12}},
 {{10, 11, 13, 14}},
 {{2, 5, 9, 12}},
 {{1, 2, 3, 5, 6, 12}}

Now I need the output matrix will be:

 A_reshaped =

    -1    -2    -2     2     0     0
    -1     2     2     2     0     0
    -1     2    -1    -2     0     0
    -1     2     0     0     0     0
     2     2     1     2     0     0
    -1    -1     2    -2     0     0
    -2    -1    -1     2     0     0
    -2    -1    -1     2     0     0
     2    -1     2    -1     0     0
     2     2    -1     2     0     0
     2     2    -1     2     0     0
     2     2    -1     2     0     0
     2     1    -1    -1     0     0
     2     2    -2     2    -2     2

Answer 1

[Matt J]

A=[  0    -1     0     0     0     0    -2    -2     0     0     0     0     0     2
    -1     0     0     0     0     0     0     0     2     0     0     0     2     2
     0     0     0    -1     2    -1     0     0     0     0     0     0     0    -2
     0     0    -1     0     2     0     0     0     0     0     0     0     0     0
     0     0     2     2     0     0     0     0     0     0     0     0     1     2
     0     0    -1     0     0     0    -1     0     0     2     0     0     0    -2
    -2     0     0     0     0    -1     0    -1     0     2     0     0     0     0
    -2     0     0     0     0     0    -1     0    -1     0     2     0     0     0
     0     2     0     0     0     0     0    -1     0     0     2     0    -1     0
     0     0     0     0     0     2     2     0     0     0    -1     2     0     0
     0     0     0     0     0     0     0     2     2    -1     0     2     0     0
     0     0     0     0     0     0     0     0     0     2     2     0    -1     2
     0     2     0     0     1     0     0     0    -1     0     0    -1     0     0
     2     2    -2     0     2    -2     0     0     0     0     0     2     0     0];
     
     
 At=A.';
 
 I0=(At~=0);
 
 I = sort(I0,1,'descend');

Areshaped=zeros(size(At));

Areshaped(I)=At(I0);

Areshaped=Areshaped(any(Areshaped,2),:)'

Areshaped = 14×6

-1 -2 -2 2 0 0 -1 2 2 2 0 0 -1 2 -1 -2 0 0 -1 2 0 0 0 0 2 2 1 2 0 0 -1 -1 2 -2 0 0 -2 -1 -1 2 0 0 -2 -1 -1 2 0 0 2 -1 2 -1 0 0 2 2 -1 2 0 0

[Nadatimuj]

Thank you!

Answer 2

[Arif Hoq]

try this:

A =[0     1     0     1     0
 1     0     1     1     0
 0     1     0     1     1
 1     1     1     0     1
 0     0     1     1     0];
output=sort(A,2,'descend');
output(:,end)=[]

output = 5×4

1 1 0 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 0 0

[Nadatimuj]

This worked for the small example I asked. However, I am sorry my original question was unclear about the adjacency where sorting breaks the adjcency list. I am clarfying my question by editing it:

A =

     0    -1     0     0     0     0    -2    -2     0     0     0     0     0     2
    -1     0     0     0     0     0     0     0     2     0     0     0     2     2
     0     0     0    -1     2    -1     0     0     0     0     0     0     0    -2
     0     0    -1     0     2     0     0     0     0     0     0     0     0     0
     0     0     2     2     0     0     0     0     0     0     0     0     1     2
     0     0    -1     0     0     0    -1     0     0     2     0     0     0    -2
    -2     0     0     0     0    -1     0    -1     0     2     0     0     0     0
    -2     0     0     0     0     0    -1     0    -1     0     2     0     0     0
     0     2     0     0     0     0     0    -1     0     0     2     0    -1     0
     0     0     0     0     0     2     2     0     0     0    -1     2     0     0
     0     0     0     0     0     0     0     2     2    -1     0     2     0     0
     0     0     0     0     0     0     0     0     0     2     2     0    -1     2
     0     2     0     0     1     0     0     0    -1     0     0    -1     0     0
     2     2    -2     0     2    -2     0     0     0     0     0     2     0     0

Now it's adjacency list will be (I got it from Mathematica):

 {{2, 7, 8, 14}},
 {{1, 9, 13, 14}},
 {{4, 5, 6, 14}},
 {{3, 5}},
 {{3, 4, 13, 14}},
 {{3, 7, 10, 14}},
 {{1, 6, 8, 10}},
 {{1, 7, 9, 11}},
 {{2, 8, 11, 13}},
 {{6, 7, 11, 12}},
 {{8, 9, 10, 12}},
 {{10, 11, 13, 14}},
 {{2, 5, 9, 12}},
 {{1, 2, 3, 5, 6, 12}}

Now I need the output matrix will be:

 A_reshaped =

    -1    -2    -2     2     0     0
    -1     2     2     2     0     0
    -1     2    -1    -2     0     0
    -1     2     0     0     0     0
     2     2     1     2     0     0
    -1    -1     2    -2     0     0
    -2    -1    -1     2     0     0
    -2    -1    -1     2     0     0
     2    -1     2    -1     0     0
     2     2    -1     2     0     0
     2     2    -1     2     0     0
     2     2    -1     2     0     0
     2     1    -1    -1     0     0
     2     2    -2     2    -2     2

[Nadatimuj]

I have also edited my original question. Thanks.

[Arif Hoq]

or try this:

A =[0    -1     0     0     0     0    -2    -2     0     0     0     0     0     2
-1     0     0     0     0     0     0     0     2     0     0     0     2     2
0     0     0    -1     2    -1     0     0     0     0     0     0     0    -2
0     0    -1     0     2     0     0     0     0     0     0     0     0     0
0     0     2     2     0     0     0     0     0     0     0     0     1     2
0     0    -1     0     0     0    -1     0     0     2     0     0     0    -2
-2     0     0     0     0    -1     0    -1     0     2     0     0     0     0
-2     0     0     0     0     0    -1     0    -1     0     2     0     0     0
0     2     0     0     0     0     0    -1     0     0     2     0    -1     0
0     0     0     0     0     2     2     0     0     0    -1     2     0     0
0     0     0     0     0     0     0     2     2    -1     0     2     0     0
0     0     0     0     0     0     0     0     0     2     2     0    -1     2
0     2     0     0     1     0     0     0    -1     0     0    -1     0     0
2     2    -2     0     2    -2     0     0     0     0     0     2     0     0];
b= size(A, 1);
[~, Y] = sort(A == 0, 2);
output= A((1:b).' + (Y - 1) * b);
output( :, ~any(output,1) ) = []

output = 14×6

-1 -2 -2 2 0 0 -1 2 2 2 0 0 -1 2 -1 -2 0 0 -1 2 0 0 0 0 2 2 1 2 0 0 -1 -1 2 -2 0 0 -2 -1 -1 2 0 0 -2 -1 -1 2 0 0 2 -1 2 -1 0 0 2 2 -1 2 0 0

[Nadatimuj]

Thanks!