D.B. West is an extremely challenging book for self study due to its terseness, much like many typical graduate level courses. For a first course in graph theory, I highly recommend "A First Course in Graph Theory" by Chartrand and Zhang (appropriately named). The exposition is lucid and beautiful, and kept to a reasonable amount. The material is also motivated, and was overall a great experience for me. This was one of the first math books I read, and I think it is quite amazing. I did have to use D.B. West's book in a later graph theory course, so I do know what using that one is like: let's just say, not fun.
For beginner graph theory, A First Course in Graph Theory by Chartrand/Zhang is pretty good.