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In this paper, we investigate the use of limited infrastructure, in the form of wires, for improving the energy efficiency of a wireless sensor network. We call such a sensor network - a wireless sensor network with a limited infrastructural support - a hybrid sensor network. The wires act as short cuts to bring down the average hop count of the network, resulting in a reduced energy dissipation per node. Our results indicate that adding a few wires to a wireless sensor network can not only reduce the average energy expenditure per sensor node, but also the non-uniformity in the energy expenditure across the sensor nodes.