Jelly,  18  16 bytes

Assumes self-connections may be any weight (i.e. they are not necessarily only either \$0\$ or the equal weight).

Jœcṗ€2EÐḟ€œị⁸E€S 

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the two subsets of size 3 being ACE and BCD
With n=2 all 10 subsets of size 2 work as its symmetric.

How?

Jœcṗ€2EÐḟ€œị⁸E€S - Link: list of lists of integers, M; integer, n J - range of length of M = [1,2,3,...,length(M)] œc - Combinations of length n e.g. [[1,2,3],[1,2,4],[1,3,4],[2,3,4]] € - for each: ṗ 2 - Cartesian power with 2 € - for each: Ðḟ - discard if: E - all-equal (i.e. diagonal co-ordinates like [3,3]) œị - multi-dimensional index into (vectorises): ⁸ - chain's left argument, M € - for each: E - all equal? S - sum