Small worlds as navigable augmented networks: Model, analysis, and validation

Abstract

The small world phenomenon, a.k.a. the six degree of separation between individuals, was identified by Stanley Milgram at the end of the 60s. Milgram experiment demonstrated that letters from arbitrary sources and bound to an arbitrary target can be transmitted along short chains of closely related individuals, based solely on some characteristics of the target (professional occupation, state of leaving, etc.). In his paper on small world navigability, Jon Kleinberg modeled this phenomenon in the framework of augmented networks, and analyzed the performances of greedy routing in augmented multi-dimensional meshes. This paper objective is to survey the results that followed up Kleinberg seminal work, including results about: - extensions of the augmented network model, and variants of greedy routing, - designs of poly log-navigable graph classes, - the quest for universal augmentation schemes, and - discussions on the validation of the model in the framework of doubling metrics. © Springer-Verlag Berlin Heidelberg 2007.