I saw your post yesterday but 'passed on by' because that image looks way too complicated for me,
But since no-one else has jumped in I thought I would come back with my own thoughts.
I'm sure there is specialised software for this type of graph, but don't know of any myself, so if I had to do this I would have 3 options to try;
1] The simplest to attempt, but perhaps trickiest to make it work and look good, I would 'cheat' and use an image editor like MSPaint. Start in the center with the connecting lines and work outwards. Then overlay the circle hubs, and finally use Paint's Text tool to add text.
2] See if Excel can do it. Excel has various graph-type options and I like working in Excel, but I am not sure if it is up to this type of graph.
3] Use Word. I think Word's AutoShapes would be useful here, but there would be a lot of learning and 'trial and error'.
I hope that helps.
I found the image below as part of a publication by Environment Canada and would love to learn how to make something similar myself.
I thought of doing this manually in illustrator or something similar of course, but to me this has the look of being done with some graphing software. If anyone has an idea of how to generate something similar with the correct data I would appreciate it.