The only possiblity I can think of is the use of "Incremental Hierarchic Layout" routing with the option "Automatic Edge Grouping" enabled. In this case yEd will place the number of connecting edges as label next to the edges. (Sorry I forgot that I did that myself).
You can add an label to the edge with the number of links (see my example). This label behaves as any label and can be formated and moved over the edge (with filled background).