When you are attempting to learn graph theory for an exam or final project, it can be difficult to find the correct text for your learning needs. There are few comprehensive texts available today but many textbooks provide an overview of the topic which might not be sufficient. Even if you do find a good text, its comprehensiveness may not suit your needs and could result in missing crucial details that could get you into trouble on assignment assessment. This article attempts to help you in your search for material by providing you with an annotated list of the best books on graph theory. These books are available at the time of this article's last update. It is not meant to be a complete list of all available material, but rather it highlights what is available today. A good book for learning graph theory begins with a solid foundation in mathematics before moving into network theory. The text should also include examples, pictures, and history of the subject to better help the reader understand how these concepts came about and how they are used today. This annotated list contains books on many different levels so you may have to look around if your math knowledge is limited. "Elementary Graph Theory" by Ron L. Graham, Donald E. Knuth, Oren Patashnik and Richard Weyhrauch is a well-known book that provides a sound mathematical basis for graph theory by developing a strong foundation in linear algebra. It begins with the fundamentals of linear algebra then progresses into the properties of graphs. The text uses many examples to help explain these ideas which makes it much easier to understand when compared to other texts which focus on detailed proofs and theorems. The second text in this list, "Graph Theory" by Paul J. Kelly, is an intermediate-level book that examines many different concepts in graph theory using many examples and illustrations throughout the book. The text begins with a history of graphs followed by an introduction to the algebra used in graph theory. The remaining chapters explore concepts such as connectivity, paths, circuits, topology and more. This list shows two advanced texts in graph theory. "Survey of Combinatorial Mathematics" by John R. Tutte provides a great overview of combinatorics and graph theory in a compendium format for researchers and specialists alike. This book contains survey articles from many renowned mathematicians that provide insight into their area of expertise such as Ramsey Theory, Matching Theory and Network Flows among many others. The second book on this list is "Introduction to Graph Theory" by William J. Floyd and Richard L. Fellows is an advanced-level book that examines the basic concepts of graph theory in greater depth. This text begins with an introduction to basic concepts like graphs, their properties and concepts like adjacency matrices followed by more detailed topics like matroid theory, spanning trees, trees in n-space and Ramsey Theory. This book was last updated in 2009. A great way to learn graph theory is by solving problems in the field. As with any field of study it can be difficult to find problems that are considered hard but once you encounter them it will be much easier to solve them because they will give you insight into the subject that you might not have had otherwise.
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