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In this paper, we consider a class of energy-aware routing algorithm that explicitly takes into account the connectivity of the remaining sensor network. In typical sensor network deployments, some nodes may be more important than other nodes because the failure of these nodes causes the network disintegration, which results in early termination of information delivery. To mitigate this problem, we propose a class of routing algorithms called keep-connect algorithms, that use computable measures of network connectivity in determining how to route packets. The proposed algorithms embed the importance of the nodes in the routing cost/metric. The importance of a node is characterized by the algebraic connectivity of the remaining graph when that node fails. We prove several properties of the proposed routing algorithm including the energy consumption upper bound. Using extensive simulations, we demonstrate that the proposed algorithm achieves significant performance improvement compared to the existing routing algorithms. More importantly, we show that our proposed algorithm is more robust in terms of algebraic network connectivity compared to the existing algorithm. Finally, we present the distributed implementation of our proposed algorithm.