Rita, goes to show one can't always believe what one reads. I've been trying to get a mulberry established inside my chicken yard primarily for them to snack on, but so far all I've done is kill them, and they are somewhat difficult for me to locate. I have a cousin on the Jersey shore who seasonablly curses the purple ones used as street trees, so perhaps they are more of a east-coast tree.
Re elderberries, my native Sambuca racemosa might be considered invasive - they pop up regularly at the edges of my woods and occasionally within my garden beds. Some I let grow, others not. For some strange reason, my husband dislikes this plant and regularly mows them with his brush hog, but they just come back up somewhere else, so I quit trying to stop him. For me, they are a great summer screen, growing to their full size in just a few years. I've never tried any cultivated sambucas, although I've sure seen some pretty ones.