Consider the following :-

a=[[0, 4, 8], [9, 0, 9], [1000, 1000, 0]]
a=Matrix(a)
 H=DiGraph(a,weighted=True)
 H.hamiltonian_path(used_edge_labels=True)

This returns (1009, Subgraph of (): Digraph on 3 vertices) but the minimum 
weight Hamiltonian path has weight 13.

I have installed sage-8.1 and my operating system is Ubuntu 14.04 LTS (64 
bit) and my processor is Intel® Core™ i5-3210M CPU @ 2.50GHz × 4 .

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