Vigsø is an island on the entrance of the Odense docks/river. there lives 3 people there, they own property there so its not government owned. This has to be an inclusion.
Vigsø is a city - not an island. If you mean Vigelsø, I couldn't find any documentation that states anything but the island being uninhabited. Remember the residence needs to be more or less permanent before the island can be considered inhabited.