I tried to use the basic formula (got it from another SO question), for calculating the max number of different edge sets, for n vertices:

2**(n*(n-1)/2)

but it's good only for small range of numbers - then it gets too complex.

Is there a way to improve this formula/reduce the complexity?

Here's an easy way to speed this up quite considerably: 2 ** x is always equal to 1 << x, so long as x is a non-negative integer; but the latter is hundreds of times faster, because it's just shifting bits rather than doing arithmetic.

>>> def slow(n):
...     return 2 ** (n * (n-1) // 2)
... 
>>> def fast(n):
...     return 1 << (n * (n-1) // 2)
... 
>>> from timeit import timeit
>>> timeit(lambda: slow(1000), number=1000)
1.5656050549987413
>>> timeit(lambda: fast(1000), number=1000)
0.005352460000722203