Searching in a Small World
Oskar J. Sandberg · 2005
The small-world phenomenon, that the world’s social network is tightly connected, and that any two people can be linked by a short chain of friends, has long been a subject of interest. Famously, the psychologist Stanley Milgram performed an experiment where he asked people to deliver a letter to a stranger by forwarding it to an acquaintance, who could forward it to one his acquaintances, and so on until the destination was reached. The results seemed to confirm that the small-world phenomenon is real. Recently it has been shown by Jon Kleinberg that in order to search in a network, that is to actually find the short paths in the manner of the Milgram experiment, a very special type of a graph model is needed. In this thesis, we present two ideas about searching in the small world stemming from Kleinberg’s results. In the first we study the formation of networks of this type, attempting to see why the kind