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Wireless Sensor Networks (WSNs) is a distributed collection of sensor nodes. These Wireless Sensor Networks have wide applications in various areas like in disaster recovery, military operation, tracking etc. In this paper, the object of study is a random graph induced by the random key pre-distribution scheme of Eschenauer and Gligor under the assumption of full visibility. Here the authors establish the threshold value of the parameters (Key pool size and key-ring of an individual node) for which the network achieve almost sure connectivity via secure links.
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