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The study of probability distributions over graphs. For example, the Erdős–Rényi model where each edge occurs independently with equal probability.
5
votes
What are some useful invariants for distinguishing between random graph models?
Any property for which there is an efficient property testing algorithm is a candidate, because such algorithms are extremely efficient.
Another approach is to note that many random graph models have …
11
votes
A Modern Proof of Erdos and Renyi's 1959 Random Graph Paper?
One reference is Chapter 5 of Random Graphs by Janson, Łuczak, and Ruciński. Their proof uses the theory of Galton–Watson branching processes, so it is not quite the same argument that Erdős a …