In undergrad I used <em>Graphs and Digraphs</em> by Chartrand, Lesniak, and Zhang. (I linked to the fifth edition since that's the one I used, but while Googling I saw the sixth edition is out now.)
Very comprehensive, reads like a pure math book. Beautifully typeset. The only thing is it might be too comprehensive: better as a reference than a self-study source. I used it alongside a class so I don't know about that last point.
If you want a textbook recommendation now that you have the name of the field, I used Graphs and Digraphs for the class I took.