Hello Robert,

For further computational exploration, you may be interested in the following functions:

FindClique can find cliques efficiently (much more efficiently than taking Subgraphs of vertex Subsets).

The IGraph/M package has the IGCliqueSizeCounts function which can count cliques of various sizes even more efficeintly. E.g.,

IGCliqueSizeCounts[graph, {3,5}]

will counts cliques between sizes 3 and 5.

Finally, I would advise against trying to use ' in variable names. While a = 1; a' = 2; appears to work and create two distinct variable, the ' is quite literally interpreted as a derivative, in this case the derivative of "1" (which is of course nonsense). Now try b=1, then evaluate b'—and you get 2 as the answer, because according to Mathematica, that is "the derivative of 1).