I assuming that you are deleting Utility Network using database connection with UN owner privileges.
To see the detail of locks you need to follow the instructions as- Manage geodatabase locks—Manage geodatabases in PostgreSQL | ArcGIS Desktop
You have to right-click the desired Object name to see the user disconnect the user.
Once you are able to disconnect all the users, simply right click the Utility Network from DB connection at Catlog view.
Then click on Delete.
Hope this will help you.