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Among security problems of sensor networks, the wormhole attack is especially a serious one because its launch is rather easy and the detection is very difficult. Beside the malicious wormholes built deliberately by attackers, this paper presents another type of wormholes: natural wormholes according to the "shortcut" property of wormholes. Natural wormholes are critical links formed by the topological result of deployment. Both types of wormholes are harmful to normal network operations and need to be identified and repaired to avoid severe damages. This paper presents two novel distributed algorithms using only local connectivity information for detecting both types of wormholes. Unlike the previous approaches, the proposed solution requires no special hardware to get location information or time synchronization.