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The Erdős–Rényi model, named after mathematicians Paul Erdős and Alfred Rényi, is a fundamental probabilistic model in graph theory. Introduced in 1959, it provides a simple yet powerful framework for studying random graphs, which are graphs formed by connecting vertices with edges chosen randomly. The model is defined by two key parameters: the number of vertices *n* and a probability *p* that determines whether any given pair of vertices is connected by an edge.
In the Erdős–Rényi model, each possible edge in a graph with *n* vertices is included independently with
The model has broad applications in network science, social sciences, and computer science, where it helps analyze
Variations of the model include the *Erdős–Rényi G(n, m)* model, where a fixed number of edges *m*