  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.
