Random graphs are mathematical structures used to model relationships between objects. They consist of a set of vertices connected by edges, where the edges are formed randomly. This randomness allows researchers to study various properties of networks, such as connectivity and clustering, which are important in fields like computer science and sociology. The study of random graphs began with the work of Paul Erdős and Alfréd Rényi in the 1950s. Their models, known as Erdős–Rényi graphs, provide a foundation for understanding how networks behave as they grow and how they can be analyzed statistically.