No, it isn’t going to strangle your dog, but it is dangerous in other ways - it is an invasive species that is choking out other plants and destroying habitat.  It requires many hands to keep it under control, so residents are encouraged to keep their eyes out for it in public greenspace and pull it out.  There will be a group dog-strangling vine removal session along Sawmill Creek in August, but meanwhile check out the Fletcher Wildlife Garden website  http://www.ofnc.ca/fletcher/research/swallowwort/index_e.php to learn more about it and join the fight against it.