What are the best resources, online or offline to learn the various algorithms related to Graph Theory, and how can a beginner learn/practise coding them?

If you're looking to work with graphs from a more practical than a theoretical aspect, then I suggest you read the basics about graphs from any popular discrete mathematics textbook, here's one that I like: Discrete Mathematics & It's Applications - Rosen http://www.mhhe.com/math/advmath/rosen/ Then maybe look at some of the more popular graph algorithms: Introduction to Algorithms - Corment et. al. http://mitpress.mit.edu/algorithms/ Then code,code,code. Some interesting Graph problems are available at the University of Vallodilid programming site (popularly known as the UVa Online Judge): http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=150 http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=303

It depends to the computer language you are using. For Java I reccomend this one http://www.amazon.com/Data-Abstraction-Problem-Solving-Java/dp/0132122308/ref=sr_1_1?s=books&ie=UTF8&qid=1348032389&sr=1-1&keywords=wall+and+mirror+java

Tarjan, Robert E. (1983). Data structures and network algorithms. Philadelphia: Society for Industrial and Applied Mathematics.ISBN 978-0-89871-187-5. OCLC 10120539.