Duncan watts and steven strogatz biography

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.

Steven Henry Strogatz is an American mathematician and author, and the Susan and Barton Winokur Distinguished Professor for the Public Understanding of.

It was proposed by Duncan J. Watts and Steven Strogatz in their article published in in the Nature scientific journal. 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 a randomized structure close to ER graphs 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. The underlying lattice structure of the model produces a locally clustered network, while the randomly rewired links dramatically reduce the average path lengths.

The three properties of interest are the average path length , the clustering coefficient , and the degree distribution. This results in a region where the average path length falls rapidly, but the clustering coefficient does not, explaining the "small-world" phenomenon. The topology of the network is relatively homogeneous, meaning that all nodes are of similar degree.

The major limitation of the model is that it produces an unrealistic degree distribution. In contrast, real networks are often scale-free networks inhomogeneous in degree, having hubs and a scale-free degree distribution. The Watts and Strogatz model also implies a fixed number of nodes and thus cannot be used to model network growth. Contents move to sidebar hide.

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