## 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 language | English |
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Article number | 036106 |

Number of pages | 5 |

Journal | Physical Review. E, Statistical, Nonlinear and Soft Matter Physics |

Volume | 68 |

Issue number | 3 |

DOIs | |

Publication status | Published - Sept 2003 |

## Keywords

- complex networks
- web