Erdős–Rényi theorem

The Erdős–Rényi theorem explores how random networks, like social or communication networks, behave as they grow large. It states that there's a critical point where increasing the number of connections between nodes (people, computers) suddenly causes the network to become connected, meaning there's a path between every pair of nodes. Below this threshold, the network remains fragmented with many isolated groups. Above it, a large "giant" connected component emerges, transforming the structure dramatically. This helps us understand phenomena like how quickly information spreads or contagious diseases can reach everyone when a certain level of connectivity is reached.