>
> Can you try using the "neighbors" keyword with something?
>
> sage: list(G.breadth_first_search(0,neighbors=lambda x: 
> sorted(G.neighbors(x))))
> [0, 8, 11, 19, 1, 12, 16, 2, 5, 9, 4, 15, 14, 18, 7, 6, 10, 13, 17, 3]
>

Except that's not right, because it lists them all.  I tried putting [0] in 
some logical places but it didn't seem to work right away - but I bet this 
will give you a good start for a final solution!

>
> Sorry for having to use the lambda function.  I'm not sure there is a 
> better way to do it.
>

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