| Summary: | Suppose that n nodes with n 0 acquaintances per node are randomly deployed in a two-dimensional Euclidean space with the geographic restriction that each pair of nodes can exchange information between them directly only if the distance between them is at most r , the acquaintanceship between nodes forms a random graph, while the physical communication links constitute a random geometric graph. To get a fully connected and secure network, we introduce secrecy transfer which combines random graph and random geometric graph via the propagation of acquaintanceship to produce an acquaintanceship graph G n , n 0 , a kind of random geometric graph with each edge representing an acquaintanceship between two nodes. We find that components of graph G n , n 0 that undergoes a phase transition from small components to a giant component when n 0 is larger than a threshold, the threshold for G n , n 0 to be a connected graph is derived. In addition, we present its implementation method and applications in wireless sensor networks.
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