*(Publicationes Mathematicae. 6: 290â€“297.)*

Original source of ErdĹ‘sâ€“RĂ©nyi model.

In the mathematical field of graph theory, the ErdĹ‘sâ€“RĂ©nyi model is either of two closely related models for generating random graphs. They are named after mathematicians Paul ErdĹ‘s and AlfrĂ©d RĂ©nyi, who first introduced one of the models in 1959,[1][2] while Edgar Gilbert introduced the other model contemporaneously and independently of ErdĹ‘s and RĂ©nyi.[3] In the model of ErdĹ‘s and RĂ©nyi, all graphs on a fixed vertex set with a fixed number of edges are equally likely; in the model introduced by Gilbert, each edge has a fixed probability of being present or absent, independently of the other edges. These models can be used in the probabilistic method to prove the existence of graphs satisfying various properties, or to provide a rigorous definition of what it means for a property to hold for almost all graphs.

hat tip: *Linked: The New Science Of Networks*Â byÂ Albert-LĂˇszlĂł BarabĂˇsi