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The sampling method has been paid much attention in the field of complex network in general and statistical physics in particular. This paper presents two new sampling methods based on the perspective that a small part of vertices with high node degree can possess the most structure information of a network. The two proposed sampling methods are efficient in sampling the nodes with high degree. The first new sampling method is improved on the basis of the stratified random sampling method and selects the high degree nodes with higher probability by classifying the nodes according to their degree distribution. The second sampling method improves the existing snowball sampling method so that it enables to sample the targeted nodes selectively in every sampling step. Besides, the two proposed sampling methods not only sample the nodes but also pick the edges directly connected to these nodes. In order to demonstrate the two methods' availability and accuracy, we compare them with the existing sampling methods in three commonly used simulation networks that are scale-free network, random network, small-world network, and two real networks. The experimental results show that the two proposed sampling methods perform much better than the compared existing sampling methods in terms of sampling cost and obtaining the true network structural characteristics.