Between Visio 2010 and yEd 3.9.2 I don't see any compatable file types, either from Visio to yEd or from yEd to Visio in which you retain your graph information.
Visio won't even let you save in Excel or CSV format (which you CAN import into yEd).
In either program you can save as a graphic and import the exported graphic into the opposite program, but that doesn't really help you so much.
GL