Rating: 
Summary: Pretty good
Review: Level of the book: 3rd-4th year undergrad or 1st-2nd year grad (pretty big range).Don't let other reviews fool you. This book does an excellent job covering the material at hand, especially given the task West set out to achieve. The book basically stands alone thanks to thorough appendices and a fair amount of examples, plus lots of problems (mostly proofs). Because this material is proof-based, I cannot suggest that this book could stand alone, but that someone else should review problems and such. When I first was reading this book, I ignored the appendices, and that was my downfall. Once I started using all the tools in this book, things started coming together. Because of the intricate design, I would recommend this book only to people who are serious about a thorough introduction to graph theory. That is, actually proving many of the theorems that play a central role in this introduction. For a simple introduction to concepts, I would recommend Trudeau's book, "Introduction to Graph Theory," which is a good read and introduces a few of the ideas and definitions of graph theory, but does not focus on proofs. My only major quarrel with this book is that it is completely void of color! This would be EXTREMELY useful in this book because many of the diagrams are complicated and different color labels would make things much clearer (instead of bolding lines and such). The increased price of the book would certainly be worth the clarity from color. There are also some typos throughout the book, but none too major (that have been noticed). Overall, I would highly recommend this book over any other, but consider waiting until an edition with color comes out.
Rating:
Summary: Pretty good
Review: Level of the book: 3rd-4th year undergrad or 1st-2nd year grad (pretty big range). Don't let other reviews fool you. This book does an excellent job covering the material at hand, especially given the task West set out to achieve. The book basically stands alone thanks to thorough appendices and a fair amount of examples, plus lots of problems (mostly proofs). Because this material is proof-based, I cannot suggest that this book could stand alone, but that someone else should review problems and such. When I first was reading this book, I ignored the appendices, and that was my downfall. Once I started using all the tools in this book, things started coming together. Because of the intricate design, I would recommend this book only to people who are serious about a thorough introduction to graph theory. That is, actually proving many of the theorems that play a central role in this introduction. For a simple introduction to concepts, I would recommend Trudeau's book, "Introduction to Graph Theory," which is a good read and introduces a few of the ideas and definitions of graph theory, but does not focus on proofs. My only major quarrel with this book is that it is completely void of color! This would be EXTREMELY useful in this book because many of the diagrams are complicated and different color labels would make things much clearer (instead of bolding lines and such). The increased price of the book would certainly be worth the clarity from color. There are also some typos throughout the book, but none too major (that have been noticed). Overall, I would highly recommend this book over any other, but consider waiting until an edition with color comes out.
Rating: 
Summary: Unclear Statements
Review: My professor gave me the section about Random Graphs to study. It nearly drove me insane; I came up with counter examples to West's theorems! Then I read the proof closely and realized West was proving the opposite of what I understood the statement to say (on more than one occaision within four pages). So, my next meeting with the prof, I asked him to translate what one of the theorems said, and he read it just the way I understood it the first time around. Now, his explanations are clear most of the time, but then West uses unnecessarily complex language too frequently.
Rating:
Summary: Unclear Statements
Review: My professor gave me the section about Random Graphs to study. It nearly drove me insane; I came up with counter examples to West's theorems! Then I read the proof closely and realized West was proving the opposite of what I understood the statement to say (on more than one occaision within four pages). So, my next meeting with the prof, I asked him to translate what one of the theorems said, and he read it just the way I understood it the first time around. Now, his explanations are clear most of the time, but then West uses unnecessarily complex language too frequently.
Rating:
Summary: Not for beginners
Review: One of the main problems of writing a textbook on graph theory is the relative immaturity of the field. Unlike, say, algebra or analysis, it is difficult to establish exactly which concepts and topics are considered part of the "canon" and where they rank in importance. Sure, matchings should be covered but is that more or less important than colouring? Should edge colourings be even considered? And so forth. There is no universally agreed upon introductory graph theory syllabus. Given this complication, I find it hard to fault this book for its seemingly slap-dash selection (and treatment) of topics. Personally, I would have preferred less on planarity and k-factors and more on coloring and random graphs. Also, I don't think that spectral graph theory and Ramsey theory belong in an introductory text. After all, why bring up these topics if you can't explore them to any intelligent degree? But again, I realize that these complaints may be petty and reflect only my personal tastes. However, what truly sinks this book are its errors. Sprinkled liberally throughout the text like chocolate chips in a Chips Ahoy cookie, these mistakes (typos?) are at times flagrant, at times subtle. In any case, it is these errors which make this book unsuitable for beginners which, judging by the subject matter, are the target audience. Unless you are already familiar with the theorems and their proofs, it is very easy to become terribly confused.
Rating: 
Summary: A great introduction
Review: Some of the criticisms leveled at West's book by other reviewers focus on either the errors that appear in the book or the choice of material. To the former concern, I would certainly add my own lamentations about the errors in the book, but note that in learning from this text I did not find the errors grevious at all and West's web page is a good guide to reading around them if you find something that cannot easily be interpreted from context (which I could not). However, the later concern I see as too nitpicking, as the book does a good job of familiarizing the reader with a large breadth of topics, to be chosen at the instructor's disscression. Just covering some subset of the book proved to be more than enough material for a challenging and well-paced one semester class, as the book was intended. I found West's literary style eminently readible, and more to the point I have been able to go on in Graph Theory with an excellent preperation thanks to West's book, which I see as the real measure of an introductory text.
The only real negative to the book is the short shrift given to more modern topics such as spectral methods and more extremal questions. The author feels a need to cram in this material, but at the cost of readability and scope. However, these topics are really not within the purvue of an undergraduate graph theory text, so I don't feel that this seriously detracts from the quality of the book. For a wonderful text on modern graph theory appropriate for a graduate student, however, let me cast my vote for Bollobas' aptly named "Modern Graph Theory".
I can't recommend West's text enough. It is modern and well written, and it serves as a great introduction to a wonderful field of mathematics.
Rating:
Summary: A great introduction
Review: Some of the criticisms leveled at West's book by other reviewers focus on either the errors that appear in the book or the choice of material. To the former concern, I would certainly add my own lamentations about the errors in the book, but note that in learning from this text I did not find the errors grevious at all and West's web page is a good guide to reading around them if you find something that cannot easily be interpreted from context (which I could not). However, the later concern I see as too nitpicking, as the book does a good job of familiarizing the reader with a large breadth of topics, to be chosen at the instructor's disscression. Just covering some subset of the book proved to be more than enough material for a challenging and well-paced one semester class, as the book was intended. I found West's literary style eminently readible, and more to the point I have been able to go on in Graph Theory with an excellent preperation thanks to West's book, which I see as the real measure of an introductory text. I can't recommend West's text enough. It is modern and well written, and it serves as a great introduction to a wonderful field of mathematics.
Rating:
Summary: Elegantly written book
Review: The author has excellently packed many important graph theory results together with numerous challenging exercises, forming a book graceful for any graph theory lover. A compact collection of advanced material into a final chapter, has made the book capable of being a reference book for the undergraduate. Do not hesitate buying it!
Rating:
Summary: Just a pile of theorems without much insight
Review: This book is an average book on graph theory. Although the author is an authority in the field, he seems to just have collected a bunch of theorems and put them together "a la" copy-and-paste, without filling up the gaps with useful insights. Intuition is always the key on a book that claims to be introductory, and this book lacks a lot of that. Probably useful as a reference book, but again not as "Introduction to Graph Theory" (and to be used as a "handbook of graph theory" it would need much more material.
Rating:
Summary: My favorite book on graph theory
Review: This book is packed full. There are 1172 problems listed, hundreds of theorems with their proofs, and helpful diagrams on almost every page. Based on my searches through a lot of math books, this is the best graph theory book around. Well-laid out, attractive, with an extensive glossary, index, and list of references. He lists the following books as his own recommendations: Introductory: Chartrand -- Graphs as Mathematical Models, Clark/Holten -- A First Look at Graph Theory, Trudeau -- Introduction to Graph Theory, Wilson -- Introduction to Graph Theory, Wilson/Watkins -- Graphs: An introductory Approach, Intermediate: Bondy/Murty -- Graph Theory with Applications, Chartrand/Lesniak --Graphs and Digraphs, Gould -- Graph Theory, Gross/Yellen -- Graph Theory, Harary -- Graph Theory, Ore - Theory of Graphs, Advanced: Berge -- Graphs, Bollobas -- Graph Theory: An Introductory Course, Bollobas -- Modern Graph Theory, Diestal -- Graph Theory, Zykov -- Fundamentals of Graph Theory. I agree with West's recommendations, but I would put West's book ahead of all of them.
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