Not sure what you mean about it being impossible for there to be a cycle.
Bram Cohen
1

The network topology itself would have cycles of course. It’s just that the construction of the HTLC cannot enforce cycles to be executed. Since all hops’ contracts are constructed with the same secret, any node that were part of a multi-hop payment twice could execute just the second contract upon receiving the secret for the first time (if that were to their advantage). On the other hand, if the network has cycles that were a net benefit to all participants, any node in that cycle could balance the cycle by sending money to themselves.

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