Classical Random Graphs

Abstract Here we give an insight into two basic models of equilibrium random networks. Often they are both called the Erdős–Rényi random graph, although, strictly speaking, this name is only for the second model. This qualitative picture is generic for random networks. The general properties of a network are primarily determined by whether or not a giant connected component is present. So the first question about any network should be about the presence and relative size of this component.