After I first made this page I have understood that the scatter of new mini-hogweeds around the sites of last year's dead flower stalks are, in the main, the result of abundant seed production, rather than any underground network - although the root stalk of the hogweed is very persistant, and does sprout buds for vegetative reproduction. From the first seedling to those huge flower stalks it takes several years - after flowering the mother plant typically dies. It's almost impossible to get rid of the giant hogweed by cutting it down. Mowing, on the other hand
(and mowing and mowing and mowing...) might do it.