I can make an application that can generate an .svg (vector graphics) with all the links and then, if you prefer jpeg format, I can convert it to jpeg.
I have a lot of experience in programming and algorithms in general, so I can write a realy fast and reliable code in C++ (or maybe C#, based on what you need) that counts every link and then draws every line correctly with the perfect thickness!
And I can make the app getting the name of each city and find the coordinates of it with google maps api to draw the line automatically in the correct position!
So.. Yes! I can make your image realy fast, with the perfect thickness!
I know, it's my first freelancer's work, i'm not such reliable, but i realy want to do that work, as perfect as i can, as beautiful as i can. I want to start doing some good works, to gain more attenction here. So I can't delude you, I have experience, I already know how to do it, I want to surprise you and getting the best feedback possible!