kisvilágjelenség

Kisvilágjelenség, often translated as "small-world phenomenon," describes a surprising characteristic found in many real-world networks, including social networks, biological systems, and technological infrastructures. It refers to the observation that even in very large networks, the average number of steps required to get from any one point to any other point is surprisingly small. This concept is often illustrated by the "six degrees of separation" idea, which suggests that any two people on Earth are connected through a chain of acquaintances with no more than five intermediaries.

The small-world phenomenon arises from a combination of local clustering and a few long-range connections. In a network exhibiting this property, most nodes are not directly connected to each other, but they tend to be part of tightly knit groups or clusters. However, a small number of "shortcut" connections exist between these otherwise separate clusters. These shortcuts dramatically reduce the path length between nodes in different groups, making the overall network much more interconnected than one might intuitively expect.

Watts and Strogatz formally introduced the small-world network model in 1998, which provided a mathematical framework for understanding this phenomenon. Their model demonstrated that by randomly rewiring a small fraction of the edges in a regular lattice, a network could transition from having long path lengths to exhibiting the small-world property. This has significant implications for understanding information diffusion, disease spread, and the robustness of complex systems.