Suppose that n nodes with [Formula: see text] 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 [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. In addition, we present its implementation method and applications in wireless sensor networks.