11 - Small World

Summary

Large real-world networks although being globally sparse, in terms of the number of edges, have their nodes/vertices connected by relatively short paths. In addition, such networks are locally dense, i.e., vertices lying in a small neighborhood of a given vertex are connected by many edges. This observation is called the “small-world” phenomenon, and it has generated many attempts, both theoretical and experimental, to build and study appropriate models of small-world networks. The first attempt to explain this phenomenon and to build a more realistic model was introduced by Watts and Strogatz in 1998 followed by the publication of an alternative approach by Kleinberg in 2000. The current chapter is devoted to the presentation of both models.