Transforming undirected trees into directed trees - Macaulay2/NautyGraphs

[Hola]

I'm working with the NautyGraphs package in Macaulay2, and I use it to generate all the undirected trees with a fixed number of vertices.

For instance:

i23 : g = generateGraphs(10, OnlyTriangleFree => true, OnlyConnected => true);
i24 : stringToGraph g_5

outputs something like:

Graph{0⇒{8,9}1⇒{8}2⇒{8}3⇒{9}4⇒{9}5⇒{9}6⇒{9}7⇒{9}8⇒{0,1,2}9⇒{0,3,4,5,6,7}}

Question: I would like to transform each graph in g into a directed rooted tree with root at vertex 0. That is, to get the output

Graph{0⇒{8,9}1⇒{}2⇒{}3⇒{}4⇒{}5⇒{}6⇒{}7⇒{}8⇒{1,2}9⇒{3,4,5,6,7}}

Any advice, suggestions, or references would be greatly appreciated!