If you notice, there is a distinct pattern to the adjacency matrices you are creating. Specifically, they are symmetric and banded. You can take advantage of this fact to easily create your matrices using the `diag`

function (or the `spdiags`

function if you want to make a sparse matrix). Here is how you can create the adjacency matrix for each case, using your sample matrix above as an example:

## 4-connected neighbors:

```
mat = [1 2 3; 4 5 6; 7 8 9]; % Sample matrix
[r, c] = size(mat); % Get the matrix size
diagVec1 = repmat([ones(c-1, 1); 0], r, 1); % Make the first diagonal vector
% (for horizontal connections)
diagVec1 = diagVec1(1:end-1); % Remove the last value
diagVec2 = ones(c*(r-1), 1); % Make the second diagonal vector
% (for vertical connections)
adj = diag(diagVec1, 1)+diag(diagVec2, c); % Add the diagonals to a zero matrix
adj = adj+adj.'; % Add the matrix to a transposed copy of
% itself to make it symmetric
```

And you’ll get the following matrix:

```
adj =
0 1 0 1 0 0 0 0 0
1 0 1 0 1 0 0 0 0
0 1 0 0 0 1 0 0 0
1 0 0 0 1 0 1 0 0
0 1 0 1 0 1 0 1 0
0 0 1 0 1 0 0 0 1
0 0 0 1 0 0 0 1 0
0 0 0 0 1 0 1 0 1
0 0 0 0 0 1 0 1 0
```

## 8-connected neighbors:

```
mat = [1 2 3; 4 5 6; 7 8 9]; % Sample matrix
[r, c] = size(mat); % Get the matrix size
diagVec1 = repmat([ones(c-1, 1); 0], r, 1); % Make the first diagonal vector
% (for horizontal connections)
diagVec1 = diagVec1(1:end-1); % Remove the last value
diagVec2 = [0; diagVec1(1:(c*(r-1)))]; % Make the second diagonal vector
% (for anti-diagonal connections)
diagVec3 = ones(c*(r-1), 1); % Make the third diagonal vector
% (for vertical connections)
diagVec4 = diagVec2(2:end-1); % Make the fourth diagonal vector
% (for diagonal connections)
adj = diag(diagVec1, 1)+... % Add the diagonals to a zero matrix
diag(diagVec2, c-1)+...
diag(diagVec3, c)+...
diag(diagVec4, c+1);
adj = adj+adj.'; % Add the matrix to a transposed copy of
% itself to make it symmetric
```

And you’ll get the following matrix:

```
adj =
0 1 0 1 1 0 0 0 0
1 0 1 1 1 1 0 0 0
0 1 0 0 1 1 0 0 0
1 1 0 0 1 0 1 1 0
1 1 1 1 0 1 1 1 1
0 1 1 0 1 0 0 1 1
0 0 0 1 1 0 0 1 0
0 0 0 1 1 1 1 0 1
0 0 0 0 1 1 0 1 0
```