Graphical evolution - Palmer, Edgar M. (John Wiley & Sons, 1985)
Subtitle: An introduction to the theory of random graphs, wherein the most relevant probability models for graphs are described together with certain thereshold functions which facilitate the careful study of the circumstances surrounding the abrupt appearance of the unique giant component which systematically absorbs its neighbors, devouring the larger first and ruthlessly continuing until the last isolated vertices have been swallowed up, whereupon the giant is suddenly brought under control by a spanning cycle. The text is laced with challenging exercises especially designed to instruct, and is accompanied by an appendix stuffed with useful formulas that everyone should know