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In this work, to obtain stronger connectivity, we propose and analyze a scheme extended by random key pre-distribution (RKP), which can work only in highly dense networks and require path construction. We investigate the threshold property of multi-hop key connectivity in random geometric networks. We have made use of the Jansonpsilas inequality to deal with the dependency overhead. Accordingly, our analysis is from a local perspective, average node degree, to describe the behavior of the entire network. Moreover,our results show that the proposed solution provides a good approximation of the empirical probability.