Extended navigability of small world networks: exact results and new insights

Details Extended navigability of small world networks: exact results and new insights Extended navigability of small world networks: exact results and new insights

2009-01-29

arxiv.org/abs/0901.4710v1

Physics

Condensed Matter

Statistical Mechanics

Presented at the BCNet Workshop in Barcelona on December 12 2008; submitted to PRL

Scientific paper

Navigability of networks, that is the ability to find any given destination vertex starting from any other vertex, is crucial to their usefulness. In 2000 Kleinberg showed that optimal navigability could be achieved in small-world networks provided that a special recipe was used to establish long range connections, and that a greedy algorithm, that ensures that the destination will be reached, is used. Here we provide an exact solution for the asymptotic behavior of such a greedy algorithm as a function of the system's parameters. Our solution enables us to show that the original claim that only a very special construction is optimal can be relaxed depending on further criteria, such as, for example, cost minimization, that must be satisfied.

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