Find equally-weighted complete graphs
Jelly,  18 16  15 bytes
Assumes self-connections may be any weight (i.e. they are not necessarily only either \$0\$ or the equal weight).
Jœcṗ2EÐḟœị³EƲ€S

Try it online!
the two subsets of size 3 being ACE and BCD
With n=2 all 10 subsets of size 2 work as its symmetric.
How?
Jœcṗ2EÐḟœị³EƲ€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:
            Ʋ   -   last four links as a monad:
   ṗ2           -     Cartesian power with 2
      Ðḟ        -     discard if:
     E          -       all-equal (i.e. diagonal co-ordinates like [3,3])
        œị      -     multi-dimensional index into:
          ³     -       program's 3rd argument (1st input), M
           E    -     all equal?
              S - sum