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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 [Formula: see text], a kind of random geometric graph with each edge representing an acquaintanceship between two nodes. We find that components of graph [Formula: see text] that undergoes a phase transition from small components to a giant component when [Formula: see text] is larger than a threshold, the threshold for [Formula: see text] to be a connected graph is derived. 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