MS&E 337 Lecture #1 Notes Information Networks Fall 2007
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چکیده
In this lecture, we will talk about the emergence of the giant component in the Erdös-Rényi random graph model G(n, p). In this model, a graph G ∈ G(n, p) on n vertices is chosen by placing an edge between each pair of vertices independently with probability p. A series of seminal paper by Erdös and Rényi from 1959-61 [1, 2, 3] helped to develop the theory behind this model. One of their key contributions was to show that several important properties of the graph had “threshold values”, above which they are almost surely true and below which they are almost surely false. Properties with threshold values are said to exhibit a “phase transition”, due to the analogous principal observed in physical systems.
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