WattsStrogatznätverk

WattsStrogatznätverk is a type of small-world network model in network theory. It was introduced by Duncan Watts and Steven Strogatz in 1998. This model aims to capture the properties observed in many real-world networks, such as social networks, biological networks, and technological networks. The key characteristic of Watts-Strogatz networks is their balance between regularity and randomness.

The Watts-Strogatz model starts with a regular lattice, where each node is connected to its nearest neighbors. For example, in a ring lattice, each node is connected to its two immediate neighbors. This regular structure provides high clustering and long path lengths between nodes. To introduce the "small-world" property, the model then randomly rewires a certain fraction of the edges. Some of the original regular connections are replaced with connections to randomly chosen nodes in the network.

This rewiring process significantly reduces the average path length between any two nodes in the network. Even a small probability of rewiring can drastically shorten the distances. Simultaneously, the Watts-Strogatz model tends to maintain a high clustering coefficient, meaning that nodes have many neighbors who are also neighbors to each other. This combination of short average path lengths and high clustering is the hallmark of small-world networks and is often observed in real-world systems. The parameter controlling the rewiring probability is crucial in determining the network's properties, interpolating between a purely regular lattice and a purely random graph.