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In a wireless multi-hop network there are a number of self-organized and decentralized wireless nodes which communicate with each other in a peer-to-peer manner over wireless channels. Each node helps in forwarding packets from source nodes to destination nodes in a multi-hop manner. In such a network, one node must establish a communication path to other nodes in order to successfully transmit and receive information. Therefore, connectivity of the wireless multi-hop network is important for accomplishing many network tasks. A widely studied problem in wireless multi-hop networks is the node density required to ensure that an arbitrarily chosen node is connected (either directly or via multi-hop path) to infinitely many other nodes with a positive probability.
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