Algorithm for the minimal cyclic connectivity (test version):

This version is slow and (unfortunateley) inaccurate. It also has, but doesn't use atoms.
The inaccuracy comes from a bug or mistake in the code, which will be fixed later.
In the future, this version can serve as a reference to compare other, faster algorithms for accuracy.


How algorithm works (there are also comments inside the code, for more details):

Step 1: Check for bridges
	Uses BridgeFinder (Tarjan's bridge-finding algorithm).
	Complexity: O(v + e)

Step 2: Enumerate all cycles
	Uses DFS (enumerate_cycles).
	In the worst case, the number of simple cycles in a graph can be exponential in v.
	Let c = number of cycles found. Each cycle is traced through the DFS stack (size <= n).
	Complexity: O(c * n)

Step 3: Try all pairs of cycles to find cyclic edge cuts
	Uses Dinic's algorithm for maximum flow.
	Number of cycle pairs = O(c^2)
	For each pair, construct a flow network and compute max flow using Dinic's algorithm.
	Max flow network has V' = v + 2 nodes and E' = 2e + 2 * cycle_length edges.
	Dinic runs in O(V'^2 * E') for general graphs. With unit capacities, it can be slightly better: O(V' * E' * log(U)).
	Each flow computation is approximately O(v^2 * e).

Total complexity:
O(v + e) + O(c * v) + O(c^2 * v^2 * e)




In future, this code will also be tailored for the BA graph repository in github.
I started it without BA graph, so I decided to first finish the logic, and then rewrite it as a full working algorithm