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We consider the network reliability problem in wireless sensor networkssecured by the heterogeneous random key predistribution scheme. This schemegeneralizes Eschenauer-Gligor scheme by considering the cases when the networkcomprises sensor nodes with varying level of resources; e.g., regular nodes vs.cluster heads. The scheme induces the inhomogeneous random key graph, denoted$\mathbb{G}(n;\pmb{\mu},\pmb{K},P)$. We analyze the reliability of$\mathbb{G}(n;\pmb{\mu},\pmb{K},P)$ against random link failures. Namely, weconsider $\mathbb{G}(n;\pmb{\mu},\pmb{K}, P,\alpha)$ formed by deleting eachedge of $\mathbb{G}(n;\pmb{\mu},\pmb{K},P)$ independently with probability$1-\alpha$, and study the probability that the resulting graph i) has noisolated node; and ii) is connected. We present scaling conditions on$\pmb{K}$, $P$, and $\alpha$ such that both events take place with probabilityzero or one, respectively, as the number of nodes gets large. We presentnumerical results to support these in the finite-node regime.

On the Network Reliability Problem of the Heterogeneous Key Predistribution Scheme