Navigability of small world networks

The “Small World Phenomenon” a.k.a. “Six Degree of Separation Between Individuals” was identified by Stanley Milgram at the end of the 60s. Milgram's 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 (occupation, state of leaving, etc.). In his seminal work, Jon Kleinberg modeled and analyzed this phenomenon in the framework of “augmented networks”. A network is navigable if it can be augmented by random links so that greedy routing performs in a polylogarithmic expected number of steps between any pair of nodes. This talk will survey the recent results in this field. In particular, the connections between navigability and low doubling dimension will be described. The possible use of the concept of navigable networks in the framework of Grid Computing and P2P networks will also be discussed.