find neighbours of neighbours

I have a matrix which represents a neighbourhood relationship of index

A=[1 2
   1 4
   2 6
   4 5
   6 7
   6 8]

A is in ascending order of A(:,1) and not including duplicate neighbours, meaning [1 2] is [2 1] is considered as the same neighbourhood relationship.

In matrix A, it means index 1 is the neighbour of 2 and 4, 2 is the the neighbour of 6, and 4 is the neighbour of 5. I want to compute a matrix B that represents the neighbours of neighbour(NON) relationship. This means 1 is the NON of 5 and 6, etc.

 B=[1 5
    1 6
    2 7
    2 8]

How can I compute such B

Answer 1

[Matt J]

I think the code below would do it, but I think your example is missing some NONs. If, as you say, [1,2] and [2,1] are equivalent, then I think 2 and 4 should be NONs because they are both neighbors of 1. Similarly, 7 and 8 both neighbor 6.

    m=max(A(:));
    Ac=sparse(A(:,1),A(:,2),true,m,m);
    Ac=double(Ac|Ac.');

    Bc=(Ac*Ac)&(~Ac);

    [i,j]=find(tril(Bc,-1));

    B=[j,i]

[Image Analyst]

It looks like he's defining it not as a "neighbor of a neighbor" if it's an immediate/adjacent neighbor. It has to be 2 layers out.

[Matt J]

Yep. My code is consistent with that. Nodes 2 and 4 are two layers apart, as are nodes 7 and 8.

[em]

This works! Thanks alot!