Stability Research On Sampling Networks With Low Probability

The stability of sampled network is a degree of consistency between the structurecharacteristics of sampled network and that of the original network. As the network sizein the real world is enormous, the cost of acquiring the data is too large, and thecomplexity of research is too big. The sampling method is used to obtain part of thenetwork and decrease the cost of research. But whether the structure of samplednetwork is in accordance with that of the original network or the sampled network canown the real structure information of the original network is a very significant question.This paper studies the stability of the sampled network with low probability. Firstly,we propose two new sampling methods, i.e., improved stratified random sampling(ISRS) and improved snowball sampling (ISBS). The two new sampling methods arebased on the Pareto rule (80/20rule),and we think that a small part of vertices withhigh node degree can possess the most structure information of a network which is alsopresented in the book titled “Linked: The new science of networks”. Besides, we alsosample the network node as well as the edge linked it. The two proposed samplingmethods are efficient in sampling the nodes with high degree. Secondly, in order todemonstrate the two methods’ availability and accuracy, we compare them with theexisting sampling methods in three commonly used simulation networks that arescale-free network, random network, small-world network, and two real networks. Weanalyse the clustering coefficient, Bonacich centrality and average path distance of thenetwork. Besides, the tests in two real networks are provided further.In conclusion, we can get that the two proposed sampling methods perform muchbetter than the compared existing sampling methods in terms of sampling cost andobtaining the true network structural characteristics. The sampled network of the twoproposed sampling methods are more stable, and we also research the differentperformance of the other sampling methods in different networks.