Are Agapanthus weeds?

from w
For a few years we have been merrily selling pots of blue apaganthus to passers-by for two to four dollars each. At this time of the year the white and blue ones are blooming profusely and residents use them for borders, driveways, and along fences in the nearby small farms. Lookin' good. But then someone said, 'Hey, you do know that they are considered weeds in some places don't you?' What? Then I read that yes, indeed, they are a menace in some places, seed easily, and get into farmland and reserves and needs to be eradicated. Hmmm. (notes from the internet as follows: Agapanthus praecox ssp.orientalis (Common agapanthus) is the name of it.
The spectacular mauve or white floral display of the Agapanthus can come at a cost. If the old flower stalks are left on the plant they will develop seed heads. This native of South Africa can spread by seed and vegetatively from fragments and runners. It is often spread in dumped garden waste and can become a nuisance in natural vegetation areas. This is one environmental weed that can be controlled by pruning off the flower heads and disposing of them responsibly.

I took two photos yesterday of two of the flowers in our front garden and also one of a quirky sign 'The Manor' which we are trying to hide by growing (very well indeed) a bouganvilliea up the wall and above the glassed-in verandah of our house. It's on a kind of Californian Bungalow really but someone before us decided 'The Manor' sounded nice!