Could any graph be turned into a small-world?

Authors:
Philippe Duchon;Nicolas Hanusse;Emmanuelle Lebhar;Nicolas Schabanel
Affiliations:
LABRI, University of Bordeaux, Bordeaux, France;LABRI, University of Bordeaux, Bordeaux, France;LIP, École Normale Supérieure de Lyon, Lyon, France;LIP, École Normale Supérieure de Lyon, Lyon, France
Venue:
DISC'05 Proceedings of the 19th international conference on Distributed Computing
Year:
2005

Citing 2
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Abstract

In the last decade, effective measurements of real interaction networks have revealed specific unexpected properties. Among these, most of these networks present a very small diameter and a high clustering. Furthermore, very short paths can be effciently found between any pair of nodes without global knowledge of the network (i.e., in a decentralized manner) which is known as the small-world phenomenon [1]. Several models have been proposed to explain this phenomenon [2,3]. However, Kleinberg showed in [4] that these models lack the essential navigability property: in spite of a polylogarithmic diameter, decentralized routing requires the visit of a polynomial number of nodes in these models.