Compile the executable with debug symbols (-g). Re-run program to trigger the segfault. Load the executable and core file that was generated when the application segfaulted into gdb and look at the backtrace.
Can't compile and test without your pqueue.h file.
Lines 73,53,93: You have memory leaks in your program. Your allocate a Graph object at line 73, Vertex at line 53 and Edge at line 93, but never delete any of them.