Audacity has added AI audio editing capabilities thanks to Intel’s free OpenVINO plugins. These plugins add AI-powered noise suppression, speech transcription, music generation and remixing, and music separation to the freeware sound editor and are available for download today.
You can see a neural net as a graph in that the neurons are connected nodes. I don’t believe that graph theory is very helpful, though. The weights are parameters in a system of linear equations; the numbers in a matrix/tensor. That’s not how the term is used in graph theory, AFAIK.
ETA: What you say about “routes” (=paths?) is something that I can only make sense of, if I assume that you misunderstood something. Else, I simply don’t know what that is talking about.
If you look at the nodes which are most likely to trigger from given inputs then you can draw paths
I still don’t know what this is supposed to mean for neural nets. I think it reflects a misunderstanding.