Combining parallel edges?

Is there a way to combine edges that are parallel? For example, if I have a node at the top and 5 nodes at the bottom linked to it, there are 5 parallel edges most of the way. Can I have a single edge (extra wide?) go most of the way to the bottom, and then split off to each of the nodes?

My current graph is very large (9530x11897 pixels @ 96 dpi); I’m using the default text size. If I wanted to print it out at full resolution, it would be 8 feet wide and 10 feet tall. (I did print it out on an 11"x17" sheet of paper, and I can barely read the text, and the lines are so thin I have a hard time even telling what colors are being used.) If parallel edges could be combined, that would make it narrower, and maybe reduce the number of horizontal lines, also making it slightly shorter.

I think this should do what you want:

Thank you for the suggestion. concentrate does almost what I want, but not quite. I want to concentrate the tails of the edges, but not the heads. I did find ranksep, which helped shrink my graph.