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You can try
T=Graph()
T.add_edges([[1,2],[2,4],[3,6],[4,8],[5,10],[6,12],[1,3],[2,5],[3,7],[4,9],[5,11],[6,13]]);
T.show(layout='tree',tree_root=1,tree_orientation='down')
The manual does not specify anything about left to right orientation so it might not be currently implemented. Edge labels are disabled by default and you can enable them with the argument edge_labels=True. You can check the manual for further details.
