WattsStrogatztype

Watts-Strogatz model, also known as the Watts-Strogatz small-world network model, is a type of random graph that is used to model complex networks. It was introduced by Duncan Watts and Steven Strogatz in 1998. The model is designed to generate networks that exhibit properties of both regular lattices and random graphs, specifically the small-world phenomenon.

The Watts-Strogatz model starts with a regular lattice, where each node is connected to its nearest neighbors. This results in a highly ordered structure. To introduce randomness, each edge in the lattice is rewired with a probability p. If p is 0, the network remains a regular lattice. If p is 1, the network becomes a random graph. For intermediate values of p, the network exhibits small-world properties, characterized by short average path lengths and high clustering coefficients.

The small-world phenomenon is observed in many real-world networks, such as social networks, the internet, and biological networks. The Watts-Strogatz model provides a simple and effective way to generate networks with these properties, making it a valuable tool in network science and complex systems research. The model has been widely studied and extended, leading to various generalizations and applications in different fields.