Standard or Top Text on Applied Graph Theory
I would take a look at the free book by Bondy and Murty: Graph Theory with Applications. This book is less-algorithmic and more graph-theoretical than other resources recommended here. There is also a newer version of the book, which is not available for free on the net, but is extremely well-written and with updated notation. In comparison to other free books on graph theory (as for example Diestel), Bondy/Murty uses a less formal approach to prove and explain the theory.

The reason I have used it, is because it is the primary text-book in the course on Graph Theory at The Technical University of Denmark, lectured by Carsten Thomassen, in which I have been assistant teacher for 2 years.