Can you suggest a good book or other resource on graphs and graph algorithms? Something that will cover some basics but also advanced problems and algorithms.
Robert Sedgewick's Algorithms in Java, Part 5 book covers Graphs.
http://www.amazon.com/Algorithms-Java-Part-Graph-Pt-5/dp/0201361213
Graph Theory with Applications by Bondy and Murty (complete pdf book available for free)
Look for Graph Theory by Narsingh Deo. Its the one that I referred to.
Graph Theory by Reinhard Diestel (free PDF online)
It's a book from the Springer series Graduate Texts in Mathematics, so it might be more of a theoretical nature than you wanted. Probably not the right place to if you just want to grab a couple of concepts and algorithms. But it is a comprehensive book on graph theory which will provide a good foundation. The first 30 pages cover the basics of graph theory, so you could limit your reading to those pages...
Introductory Graph Theory is more of a math book than CS, but it helped me get through advanced algorithms.