In your removal branch you re-tie() the iterators:
boost::tie(vi, vi_end) = boost::vertices(m_graph);
This will cause the loop to restart every time you restart the loop. This is exactly Schlemiel The Painter.
I'll find out whether you can trust remove_vertex not triggering a reallocation. If so, it's easily fixed. Otherwise, you'd want an indexer-based loop instead of iterator-based. Or you might be able to work on the raw container (it's a private member, though, as I remember).
Update Using vecS as the container for vertices is going to cause bad performance here:
If the VertexList template parameter of the adjacency_list was vecS, then all vertex descriptors, edge descriptors, and iterators for the graph are invalidated by this operation. <...> If you need to make frequent use of the remove_vertex() function the listS selector is a much better choice for the VertexList template parameter.
This small benchmark test.cpp compares:
with -DSTABLE_IT (listS)
$ ./stable
Generated 100000 vertices and 5000 edges in 14954ms
The graph has a cycle? false
starting selective removal...
Done in 0ms
After: 99032 vertices and 4916 edges
without -DSTABLE_IT (vecS)
$ ./unstable
Generated 100000 vertices and 5000 edges in 76ms
The graph has a cycle? false
starting selective removal...
Done in 396ms
After: 99032 vertices and 4916 edges
using filtered_graph (thanks @cv_and_he in the comments)
Generated 100000 vertices and 5000 edges in 15ms
The graph has a cycle? false
starting selective removal...
Done in 0ms
After: 99032 vertices and 4916 edges
Done in 13ms
You can clearly see that removal is much faster for listS but generating is much slower.