I'm trying to create something similar to this.

So, 3 different Node classes, and a whole bunch of relationships between them. In my case, there should be roughly half of the number of nodes present at most.
What I'm looking for is recommendations as to the best way to create a similar type of graph. Spent some time looking at R/GGplot2, but haven't found any solutions so far. I expect it's because I'm not using the correct vocabulary.
The posted image was created using a proprietary app that I unfortunately am not able to leverage, otherwise I'd simply use that.
Any suggestions/solutions would be fantastic! Thanks in advance.