The Erdős–Rényi model is a mathematical framework used to study random graphs. It was developed by mathematicians Paul Erdős and Alfréd Rényi in the late 1950s. In this model, a graph is created by connecting nodes randomly, where each possible edge between nodes has a fixed probability of being included. This approach helps researchers understand the properties of networks, such as connectivity and the distribution of paths. One key feature of the Erdős–Rényi model is its simplicity, allowing for easy analysis of graph behavior. As the number of nodes increases, the model reveals critical thresholds for connectivity, leading to the emergence of a giant component. This insight has applications in various fields, including computer science, biology, and social networks.