On the searchability of small-world networks with arbitrary underlying structure

Revisiting the “small-world” experiments of the ’60s, Kleinberg observed that individuals are very effective at constructing short chains of acquaintances between any two people, and he proposed a mathematical model of this phenomenon. In this model, individuals are the nodes of a base graph, the square grid, capturing the underlying structure of the social network; and this base graph is augmented with additional edges from each node to a few long-range contacts of this node, chosen according to some natural distance-based distribution. In this augmented graph, a greedy search algorithm takes only a polylogarithmic number of steps in the graph size. Following this work, several papers investigated the correlations between underlying structure and long-range connections that yield efficient decentralized search, generalizing Kleinberg’s results to broad classes of underlying structures, such as metrics of bounded doubling dimension, and minor-excluding graphs. We focus on the...

• Type: Conference
• Year: 2010
• Where: STOC
• Authors: Pierre Fraigniaud and George Giakkoupis
• Keywords: Base Graphs, Long-range Contact, Social Network, STOC 2010