Rado graph – Infinite graph containing all countable graphs, the graph formed by extending the G(n, p) model to graphs with a countably infinite number of vertices. Unlike in the finite case, the result of this infinite process is (with probability 1) the same graph, up to isomorphism.

Dual-phase evolution – Process that drives self-organization within complex adaptive systems describes ways in which properties associated with the Erdős–Rényi model contribute to the emergence of order in systems.

Exponential random graph models – statistical models for network analysis describe a general probability distribution of graphs on "n" nodes given a set of network statistics and various parameters associated with them.

Stochastic block model, a generalization of the Erdős–Rényi model for graphs with latent community structure

Watts–Strogatz model – Method of generating random small-world graphs

Barabási–Albert model – Scale-free network generation algorithm