I saw a tweet from @CompSciFact (John Cook) pointing out Luc Devroye’s (McGill University) Non-Uniform Random Variate Generation (Springer-Verlag, New York, 1986) was available for free download.
Amazon lists used copies starting at $180.91 and one new copy for $618.47, so you are better off with the scanned PDF, unless you are simply trying to burn up grant funding before the end of a year.
Chapter XIII. RANDOM COMBINATORIAL OBJECTS includes random graphs and notes:
Graphs are the most general comblnatorlal objects dealt wlth In this chapter. They have appllcatlons In nearly all flelds of sclence and englneerlng. It is qulte impossible to glve a thorough overvlew of the dlfferent subclasses of graphs, and how objects In these subclasses can be generated uniformly and at random. Instead, we will just glve a superflclal treatment, and refer the reader to general principles or speclflc artlcles In the literature whenever necessary.
For one use of random graphs in topic maps work, see the Random Graph Generator in Wandora.