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Finite differences in a small world

Higham, D.J. (2003) Finite differences in a small world. In: Proceedings of the 20th Biennial Conference on Numerical Analysis, Dundee. University of Dundee, Dundee, pp. 81-84.

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Abstract

Many complex networks in nature exhibit two properties that are seemingly at odds. They are clustered - neighbors of neighbors are very likely to be neighbors - and they are small worlds - any two nodes can typically be connected by a relatively short path. Watts and Strogatz [17] referred to this as the small world phenomenon and proposed a network model that was shown through simulation to capture the two properties. The model incorporates a parameter that interpolates between fully local and fully global regimes. As the parameter is varied the small world property is roused before the clustering property is lost.