Black Swallowwort
Cynanchum louiseae a.k.a Vincetoxicum nigrum (CISMA, GoBotany, Wikipedia, USDA) is a twining, unbranched, perennial vine. Leaves are opposite, with smooth edges and a pointed tip. It has dark purple flowers, with five triangular petals.
Removal
Black Swallowwort should be removed from the ground by digging up its rhizomes so that the plant cannot reproduce. The vine has an extensive rhizome system which must be completely removed to prevent new shoots from growing. Trying to remove the vine by pulling will often cause the plant to detach from its rhizome, allowing the vine to continue to grow new shoots. Seed pods must be disposed of carefully, to avoid inadvertently spreading the seeds to new areas.
Removed plant material should be bagged, labelled, and provided to the Acton Natural Resources department for disposal.
Mowing does not stop growth, but it does stop the generation of seeds and subsequent spreading.
Common Mis-identifications
It is sometimes confused with Pale Swallowwort (Cynanchum rossicum, Wikipedia) which is also an invasive plant.