Auto comment: topic has been updated by dawnmist00 (previous revision, new revision, compare).

DMOJ has some good ones. You can click the column header Types here to find the problems related to graph theory. For example, there are problems meant to be solved with Dijkstra's, BFS (there's a little trick to that problem), and cycle detection.

You can also look for the categories graph, bfs, etc. on A2 Online Judge.

you can use uva toolkit and find some easy to hard graph related problem in uva online judge

http://uvatoolkit.com/problemssolve.php

search for "graph"

also there are many good problems on spoj

http://www.spoj.com/problems/SHPATH/

http://www.spoj.com/problems/EZDIJKST/

http://www.spoj.com/problems/COMPANY/

http://www.spoj.com/problems/BOTTOM/ (i love this one)

http://www.spoj.com/problems/PT07X/

http://www.spoj.com/problems/PT07Y/

http://www.spoj.com/problems/PT07Z/

http://www.spoj.com/problems/MST/

and more ...

you can also use spoj tag (it's not completed yet but it's useful)

http://www.spoj.com/problems/tags