Hi Karen:
Yes, this shrub species, glossy buckthorn (Rhamnus frangula), is highly invasive.
Furthermore, the Illinois Exotic Weed Act prohibits the purchase, sale, offer to sell, distribution or planting of Japanese honeysuckle, multiflora rose, purple loosestrife, kudzu and six species of buckthorn: common buckthorn, glossy buckthorn, saw-toothed buckthorn, dahurian buckthorn, Japanese buckthorn, and Chinese buckthorn.