I am a graduate student in Economics. I have a decent grounding in maths, but I've never studied graph theory or combinatorics. I need to study graph theory in order to analyse production networks. Each node is a firm that supplies goods to other firms. Hence this is a weighted digraph. I need to be able to model the evolution of these networks based on given initial conditions, analyse flows and find fixed points and on this basis form some idea of equilibrium.
On this basis, what would be the best textbook for me? Cost is no issue, I'm going to borrow it from the library.
Here is a good beginners graph theory note (see https://homepages.warwick.ac.uk/~masgax/Graph-Theory-notes.pdf). It was designed for a fourth year undergraduate (equivalent to a Masters) module in Mathematics at the University of Warwick. It gives a good insight to graph theory that will be important in giving you a very good exposure.
There are also a number of good graph theory texts available for free at http://www.freebookcentre.net/Mathematics/Graph-Theory-Books.html. You may want to check them out also, and see the one that certify your curiosity more.
Have fun studying Graph theory!