a algorithm HFFSM based on FFSM is presented. First equally convert directed multigraphs to undirected simple graphs, and then construct suboptimal CAM tree and mine frequent subgraphs with the top-down depth-first method. The empirical study shows that HFFSM can deal with directed multigraphs well, reduce false alarms when the algorithm is applied, and is a little better than FFSM in efficiency, but more useful than FSSM