You can encourage them to stay by feeding them a mixture of poultry layer pellets and cracked corn, lettuce and some bread. If the swans are not use to people, you may have to drop the food in the water where they can find it. Once the swans find the food, slowly introduce yourself by slowly showing them that you are the source of the food. Just make sure you place the food in shallow water and in an area free from predators, I.e. no dogs, cats or wild animals. No, swans nor their eggs are a good food source. Swans are bottom feeders and this bottom feeding would be what you would be ingesting, Not Good! The Regal Swan