The most common misconception about the Lightning Network is that you need a channel open to whoever you're paying. You don't. You need ONE channel to anyone, and the network routes the payment through the graph for you.

Inside the graph: payments hop through intermediaries. Alice pays Ivy by sending through Bob, then Eve, then Grace. Each hop only sees the previous hop and the next hop; never the full route, never Alice's identity, never Ivy's. That's onion encryption, borrowed from Tor and adapted for atomic payments.

The atomic part matters. A Lightning payment is built around an HTLC chain, hashed time-locked contracts that link the hops together. Either every hop along the route settles, or every hop reverts. There is no halfway state where Bob has Alice's money but Eve never got hers. The cryptography won't allow it.

Where it fails in practice: liquidity. You can't push more BTC through a hop than that hop's outbound capacity. Routing nodes that keep their channels balanced are valuable; routing nodes that don't are useless to the network even if their channels are large. Most payment failures are liquidity failures, not connectivity failures.