### Abstract

We consider a large-scale of wireless ad hoc networks whose nodes are distributed randomly in a two-dimensional region Ω. Given n wireless nodes V, each with transmission range r_{n}, the wireless networks are often modeled by graph G(V,r_{n}) in which two nodes are connected if their Euclidean distance is no more than r_{n}. We show that, for a unit-area square region Ω, the probability G(V, r_{n}) being k-connected is at least e^{-e-α} when nπr_{n}^{2} ≥ ln n + (2k- 3) ln ln n - 2 ln(k - 1)! + 2α for k > 1 and n sufficiently large. This result also applies to mobile networks when the moving of wireless nodes always generates randomly and uniformly distributed positions. We also conduct extensive simulations to study the practical transmission range to achieve certain probability of k-connectivity when n is not large enough. The relation between the minimum node degree and the connectivity of graph G(V, r) is also studied.

Original language | English |
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Pages (from-to) | 453-457 |

Number of pages | 5 |

Journal | IEEE International Conference on Communications |

Volume | 1 |

DOIs | |

State | Published - 18 Jul 2003 |

Event | 2003 International Conference on Communications (ICC 2003) - Anchorage, AK, United States Duration: 11 May 2003 → 15 May 2003 |

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## Cite this

*IEEE International Conference on Communications*,

*1*, 453-457. https://doi.org/10.1109/ICC.2003.1204218