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Wireless Sensor Networks (WSNs) consist of many independent sensor/processing elements that are highly interactive to reach a unifying goal. Providing a suitable infrastructure for this interaction is the first step to support intra-network processing. Such underlying infrastructure should also scale well with network properties, prolong the network life and balance the load among sensors as much as possible. In this paper, we propose a novel distributed adaptive spanning tree based on Markov property interpretation in WSNs that not only enables consensus processing, but also improves network performance. The tree is constructed using a new energy efficient coverage cost and distributed Voronoi Tessellation. The utility of the proposed approach is illustrated by applying this interaction architecture for data gathering tasks in WSNs.