ErdsRényimodellen

ErdsRényimodellen, also known as the Erdős–Rényi model, is a fundamental concept in network science used to describe the random generation of graphs. It is a generative model that posits a graph with a fixed number of vertices, where each possible edge between any two vertices is present with an independent probability. There are two main variations of this model. In the G(n, p) model, a graph is constructed by selecting n vertices and then, for every pair of distinct vertices, an edge is included between them with probability p, independently of all other pairs. The number of edges in the resulting graph is not fixed but is a random variable. In the G(n, M) model, a graph is constructed by selecting n vertices and then choosing exactly M edges uniformly at random from the set of all possible edges. In this variation, the number of edges is fixed at M. The Erdős–Rényi model is widely used as a baseline for studying the properties of random networks, such as connectivity, the presence of cliques, and degree distributions. It provides a theoretical framework for understanding how macroscopic properties of networks emerge from probabilistic rules of edge formation. Despite its simplicity, the Erdős–Rényi model has proven to be a powerful tool for initial investigations into the structure and behavior of large-scale networks.