First, I like this book and gave it 5 stars.. But it is not the best book on graph theory, though it is a great intro.And really that is all the book claims to be: an intro designed to really excite the student about graph theory.Where this book shines is the presenation of a wide variety of applications, examples, and exercises. Not only the classic examples that every book uses, but alot of great applied problems, and a ton of them.I do agree with another review that the book does seem to go off track a bit and enter the land of discrete math. Yes, there are a number of graphy theory books that cover combinatorics/discrete concepts as well, but they mention that in the title. And what it does seem to cover is very topical and really does not seem to fit.However, this is a great intro to graph theory, and it does have a mix of proof/theorem without losing its approachable appeal to students starting out.Overall it is a great Dover book.