Have you actually been to the nest to confirm there are no eggs?

Here is what we are thinking may have occurred.

1. The male and female began nest building and mating. Then, something happened to the male. In the meantime, the female was pregnant and began laying and sitting on eggs. Your count is not the same as the swan's. She will begin incubating after the last egg has been laid, so she realistically may not have begun sitting for 1-2 weeks as eggs are usually, not always, but usually laid every other day. Then, sits on the nest for 35-45 days.

She is leaving the nest at night to also bathe, preen and feed and other times when you may not be constantly watching. As hatching becomes imminent, she will stay closer to the nest to bathe, rest and feed. She will also spend even less time off the nest. The moving of her legs is to straddle the eggs so she does not crush them. She is carrying material away from the nest to keep it tidy. Swans know when
an egg is viable. They are not going to sit for too long if something is not going to hatch, which leads us to believe she was actually pregnant before laying the eggs.

2. Having said the above, the only other possibility is that a female swan will still lay eggs regardless of having a male due to increased hormone levels during mating season. She laid the eggs the same way as described above and is still in the incubation period. Give her at least another week and let us know. Otherwise, try to look into the nest without disturbing her or the nest to see if there are eggs. The Regal Swan