On the Phase Transition Width of k-Connectivity in Wireless Multi-Hop Networks

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Executive Summary

Wireless multi-hop networks have been extensively investigated and discussed in recent years. Generally, a wireless multi-hop network, e.g., wireless ad hoc network or wireless sensor network, consists of a group of nodes that communicate with each other over wireless channels. The nodes in such a network operate in a decentralized and self-organized manner and each node can, if needed, act as a router to forward traffic towards its destination. For such wireless multi-hop networks, connectivity (or 1- connectivity) is a prerequisite for providing many network functions.

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