New to Java

Hello
I have a symmetric graph and a distance variable 1 or 2 etc:

| A | B | C | D
-----------------
A | 0 | 2 | 4 | 1
B | 2 | 0 | 3 | 5
C | 4 | 3 | 0 | 1
D | 1 | 5 | 1 | 0
------------------

I wanted to find different Graph Edges that are on the same Set for a give distance variable. For the Distance Variable 1, the Set will be {A, D,C}. For Distance Variable 2, it will be {A, B, C, D}, the same for Distance variable 3, 4 and 5.

Please, I need some tips on how to go about it. What is the best algorithm to solve such problem? Is there any Java Graph API for that?

Thanks,

Jona_T