Menger's theorem

Exactly.

That distinction is vital, and it sets the stage for what is arguably one of the most profound and foundational theorems in structural mathematics, Menger's theorem.

Deistel unpacks this in theorem 3.3.6, and it provides a dual perspective that bridges the gap between destroying a network and building one.

Yeah.

They are entirely parallel, distinct highways from point A to point B.

Yes.

Menger's theorem establishes a perfect duality.

It states that if an adversary needs exactly five targeted vertex strikes to sever the communication between a command center and a satellite base, it guarantees with absolute mathematical certainty that there are exactly five completely distinct, non-overlapping communication lines currently running between them.