One natural way to model human networks, such as social networks, transportation networks, or the internet, is with random graphs.
This paper summarizes the foundations of random graph theory, developed by Paul Erd¨os and Alfred R´enyi in 1958, and some common
techniques used to analyze random graphs. Three more generalized
random graph models are also explored: the configuration model, the
small-world model, and the preferential attachment model. The similarity of these models to human networks is evaluated based on four
criteria: average path length, degree distribution, clustering coefficient, and static or dynamic nature of the graph.
The textbook Analytic Combinatorics by Philippe Flajolet and Robert Sedgewick enables precise quantitative predictions of the properties of large combinatorial structures.