TITLE: New trends in Applied Graph Theory
QUESTION [5 upvotes]: What are current trends in Applied Graph Theory? I am interested mainly in non-algorithmical problems. Maybe even in applications of graphs to other mathematical disciplines. For example, abstract algebra naturally produces the notion of non-commuting graph of a group and prime graph of a ring. 
Also, what about modern Chemical Graph Theory? Is it still bounded by finding upper and lower bounds on graph indexes like Wiener's, Zagreb's, Randic's and other?
Finally, what graph-theoretical problems arose say from biological networks or from the study of social graphs?

Clearly I am not specific on this question. Sorry for that! However, I have strong interest in graphs applications, so I had to ask mathoverflowers something like that! Also, thanks for your answers!

REPLY [5 votes]: The book "Networks, Crowds, and Markets: Reasoning About a Highly Connected World" by David Easley and Jon Kleinberg contains amazing material and it is very readable. One can download a copy:
http://www.cs.cornell.edu/home/kleinber/networks-book/

REPLY [3 votes]: One relatively new area is studying the spread of infectuous diseases via graph models, with arcs representing contacts.
For example:

"Using network properties to predict disease dynamics on human contact networks."
  Proc. Royal Society B. 2011. (journal link)