Looking at your question, I feel you want to mean that there's a map where you begin at one place and also end at the same. I think it happens for some event/sport.

Cycle does not fit and loop refers more to a shape than what you probably want. Okay...

One of the common words used for this is ...

circuit - A roughly circular line, route, or movement that starts and finishes at the same place

You may also use track but I don't think it starts and ends at the same point whereas circuit does probably because the electronic circuit happens only when it completes its path.

Looking at your question, I feel you want to mean that there's a map where you begin at one place and also end at the same.

Cycle does not fit and loop refers more to a shape than what you probably want. Okay...

One of the common words used for this is ...

circuit - A roughly circular line, route, or movement that starts and finishes at the same place

You may also use track but I don't think it starts and ends at the same point whereas circuit does probably because the electronic circuit happens only when it completes its path.