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I'm trying to solve a riddle, where one part is a drawing of a complete graph of 7 vertices. I guess that part of the riddle should correspond to a number somewhere not too far from 6000.

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Does anyone know any property of a graph that can be applied to get to a number in that magnitude?

Cause the only thing I've found, is number of edges, which is way to few, and number of possible paths (2^21) which is way to high..

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    How about $7!=5040$? That’s the number of Hamilton paths (paths that start visit each vertex exactly once). – 2017-01-09
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    Yes! That was the missing piece. Now, I'll just have to read up on this Hamilton path to understand what that is :-) – 2017-01-09

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