Searching in small-world networks

Research output: Contribution to journalArticle

31 Citations (Scopus)

Abstract

We study the average time it takes to find a desired node in the Watts-Strogatz family of networks. We consider the case when the look-up time can be neglected and when it is important, where the look-up time is the time needed to choose one among all the neighboring nodes of a node at each step in the search. We show that in both cases, the search time is minimum in the small-world regime, when an appropriate distance between the nodes is defined. Through an analytical model, we show that the search time scales as N1/D(D+1) for small-world networks, where N is the number of nodes and D is the dimension of the underlying lattice. This model is shown to be in agreement with numerical simulations.

Original languageEnglish
Article number036106
Number of pages5
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Volume68
Issue number3
DOIs
Publication statusPublished - Sep 2003

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Small-world Network
Vertex of a graph
Small World
Time-average
Analytical Model
Time Scales
Choose
Numerical Simulation
simulation

Keywords

  • complex networks
  • web

Cite this

Searching in small-world networks. / de Moura, A P S ; Motter, A E ; Grebogi, C .

In: Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, Vol. 68, No. 3, 036106, 09.2003.

Research output: Contribution to journalArticle

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AB - We study the average time it takes to find a desired node in the Watts-Strogatz family of networks. We consider the case when the look-up time can be neglected and when it is important, where the look-up time is the time needed to choose one among all the neighboring nodes of a node at each step in the search. We show that in both cases, the search time is minimum in the small-world regime, when an appropriate distance between the nodes is defined. Through an analytical model, we show that the search time scales as N1/D(D+1) for small-world networks, where N is the number of nodes and D is the dimension of the underlying lattice. This model is shown to be in agreement with numerical simulations.

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