Why has this been submitted, I mean I've seen few versions of "calculus on graphs", is it because of the "translation" of analysis to graph theory? Could the submitter explain their interest in this and why they think its relevant?
Somewhat related, but my old PhD supervisor had a very interesting paper on extending some ideas from Riemannian geometry to graphs. <a href="http://arxiv.org/abs/1011.5898" rel="nofollow">http://arxiv.org/abs/1011.5898</a>
I spent a summer as an undergrad doing research on this sort of thing, a nice paper came out of it from the grad students working with us [0].<p>I love to see graph theory creeping into other branches of mathematics, especially blending the discrete and continuous domains.<p>0 - <a href="https://books.google.com/books?id=J65sAwAAQBAJ&pg=PA15&lpg=PA15&source=bl&ots=WFVXAqq8dd&sig=DZiKvOzQAp7V7V44Qd2ZvqJzj5Q&hl=en&sa=X&ved=0CDoQ6AEwBTgKahUKEwiS5tOYo7vHAhXKMIgKHa-2D8k#v=onepage&q&f=false" rel="nofollow">https://books.google.com/books?id=J65sAwAAQBAJ&pg=PA15&lpg=P...</a>