We analyze the relationship between energy consumption and topology in wireless microsensor networks. Energy consumption is the total energy required for a message to be delivered to a destination microsensor from a source microsensor. We first consider the factors in energy consumption -radio propagation models, the topology of microsensors, the probability of connectivity between microsensors and etc. The radio propagation model tells us how much energy the environment of message propagation

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... equires, and the topology is the logical configuration among microsensors. We analyze the energy consumption from two different aspects: the propagation model and the topology. A propagation model may consume more energy than that of another model at the same topology, or, different topologies may require different amounts of energy in the same propagation model. The result of analysis shows that the consumed energy is in proportion to the number of neighbors, i.e. when the topology has fewer neighboring microsensors, it consumes less energy even though it must experience more hops to the destination. We also prove that the same result can be applied to any of the radio propagation models -such as free space propagation, urban area, obstructed in building, and etc. From the two analyses in the propagation model and topology, we can conclude that when a message goes to the destination of multihop, the topology with fewer neighboring microsensors consumes less energy than that of more neighbors. We also perform a simple analysis on the connectivity among microsensors as one of the energy consumption factors. Microsensors are prone to be disconnected by microsensor failures, temporary broken links, going into sleep mode, and etc. The disconnection requires an alternative path to the destination and (or) retransmission of the same message to the next microssensor, which consumes additional energy.