Hello.  I´m using Sage to teach some network algorithms. The strange thing is 
that when I define a graph using the weighted adjacency matrix, I'm able to get 
the min_spanning_tree but not the shortest path. However, when I define the 
graph using the dictionary form, everything works OK. Here's what I mean:

sage: B = 
{0:{1:2,2:5,3:4},1:{2:2,4:7},2:{3:1,4:4,5:3},3:{5:4},4:{5:1,6:5},5:{6:7}}
sage: grafo3 = Graph(B,weighted=True)
sage: grafo3.min_spanning_tree(check=True)
   [(2, 3, 1), (4, 5, 1), (0, 1, 2), (1, 2, 2), (2, 5, 3), (4, 6, 5)]
sage: grafo3.shortest_path(0,6,by_weight=True)
 [0, 1, 2, 5, 4, 6]

so far so good, everything is as expected. Now I will define other graph using 
the weighted adjacency matrix from the previous graph

sage: matad = grafo3.weighted_adjacency_matrix()
sage: grafo4 = Graph(matad,format = "adjacency_matrix", weighted=True)
sage: grafo4.min_spanning_tree(check=True)
  [(2, 3, 1), (4, 5, 1), (0, 1, 2), (1, 2, 2), (2, 5, 3), (4, 6, 5)]

with min_spanning_tree there is no problem, but now with shortest path:

sage: grafo4.shortest_path(0,6,by_weight=True)
  Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_104.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" 
+ 
_support_.preparse_worksheet_cell(base64.b64decode("Z3JhZm80LnNob3J0ZXN0X3BhdGgoMCw2LGJ5X3dlaWdodD1UcnVlKQ=="),globals())+"\\n");
 execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmpBOCDxN/___code___.py", line 3, in <module>
    exec compile(u'grafo4.shortest_path(_sage_const_0 ,_sage_const_6 
,by_weight=True)
  File "", line 1, in <module>
    
  File 
"/usr/lib/sagemath/local/lib/python2.7/site-packages/sage/graphs/generic_graph.py",
 line 12265, in shortest_path
    L = self._backend.bidirectional_dijkstra(u,v)
  File "c_graph.pyx", line 2341, in 
sage.graphs.base.c_graph.CGraphBackend.bidirectional_dijkstra 
(sage/graphs/base/c_graph.c:15964)
TypeError: a float is required


I tried defining the weighted adjacency matrix myself for other graphs and I 
always get the same error whith shortest path, is this a bug or am I missing 
something?  Thank you very much for your help.

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