[boost] BGL - cycles in an undirected graph

Hi all, my task is to find cycles in an undirected graph and to assign a cycle id to each vertex in this cycle. It is still a bit more complicated, because I do not need just the simple cycles, but all simple cycles which are sharing edges, must get the same cycle id. I think this problem is already solved somewhere, but I cann not find the right approach, thus I am asking here if somebody have an idea how to solve it best with BGL. I think the brute force approach will work, but as the application needs to be very fast, I think I can not go this way. With brute force I mean, to collect all edges of each simple cycle and than check which are intersecting. Thanks, Michal