Watts and Strogatz model
The Watts–Strogatz model is a random graph generation model that produces graphs with small-world properties, including short average path lengths and high clustering. It was proposed by Duncan J. Watts and Steven Strogatz in their joint 1998 Nature paper. The model also became known as the (Watts) beta model after Watts used to formulate it in his popular science book Six Degrees.
The formal study of random graphs dates back to the work of Paul Erdős and Alfréd Rényi. The graphs they considered, now known as the classical or Erdős–Rényi (ER) graphs, offer a simple and powerful model with many applications.
However the ER graphs do not have two important properties observed in many real-world networks:
The Watts and Strogatz model was designed as the simplest possible model that addresses the first of the two limitations. It accounts for clustering while retaining the short average path lengths of the ER model. It does so by interpolating between an ER graph and a regular ring lattice. Consequently, the model is able to at least partially explain the "small-world" phenomena in a variety of networks, such as the power grid, neural network of C. elegans, and a network of movie actors. In 2015, researchers from the California Institute of Technology and Princeton University showed that the Watts and Strogatz model explains fat-metabolism communication in budding yeast.
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