> I expect cliques of hundreds of members, if not thousands.

the default approach seems to be the Bron–Kerbosch algorithm

From the complexity estimates given there, a worst case of at least 3**(1000/3) = 7.609e+158 for cliques of size 1000 is to be expected. °

I.o.W. you should already reserve a table at the The Restaurant at the End of the Universe to take a break in between.

Another approach would be porting Perl to quantum computers and hoping that Google and IBM are producing more than vapor ware in your lifetime.

Cheers Rolf
(addicted to the Perl Programming Language :)
Wikisyntax for the Monastery FootballPerl is like chess, only without the dice

update Nov 29

°) for the vertex-ordering version

from Degeneracy_(graph_theory)#Relation_to_other_graph_parameters

A k-degenerate graph has chromatic number at most k + 1; this is proved by a simple induction on the number of vertices which is exactly like the proof of the six-color theorem for planar graphs. Since chromatic number is an upper bound on the order of the maximum clique, the latter invariant is also at most degeneracy plus one.

In reply to Re^3: Sub set where all are connected by LanX
in thread Sub set where all are connected by Sanjay

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