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Does the following not work for getting it as a Sage graph?

sage: Z = Graph(h)
sage: Z.order() == Z.size()+1
True  # we hope!

Sage also has a minimum spanning tree method though I think it is an LP one, not the networkx one.

Your question about csv remains unanswered, largely because I didn't know there was a standard way to represent graphs in csv-file format.