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Many sensor network applications are tightly coupled with the geometric environment where the sensor nodes are deployed. The topological skeleton extraction for the topology has shown great impact on the performance of such services as location, routing, and path planning in wireless sensor networks. Nonetheless, current studies focus on using skeleton extraction for various applications in wireless sensor networks. How to achieve a better skeleton extraction has not been thoroughly investigated. There are studies on skeleton extraction from the computer vision community; their centralized algorithms for continuous space, however, are not immediately applicable for the discrete and distributed wireless sensor networks. In this paper, we present a novel Connectivity-bAsed Skeleton Extraction (CASE) algorithm to compute skeleton graph that is robust to noise, and accurate in preservation of the original topology. In addition, CASE is distributed as no centralized operation is required, and is scalable as both its time complexity and its message complexity are linearly proportional to the network size. The skeleton graph is extracted by partitioning the boundary of the sensor network to identify the skeleton points, then generating the skeleton arcs, connecting these arcs, and finally refining the coarse skeleton graph. We believe that CASE has broad applications and present a skeleton-assisted segmentation algorithm as an example. Our evaluation shows that CASE is able to extract a well-connected skeleton graph in the presence of significant noise and shape variations, and outperforms the state-of-the-art algorithms.