Efficient Random Walk based Sampling with Inverse Degree

Abstract: Random walk sampling methods have been widely used in graph sampling in recent years, while it has bias towards higher degree nodes in the sample. To overcome this deficiency, classical methods such as MHRW design weighted walking by repeating low-degree nodes while rejecting high-degree nodes, so that the long-term behavior of Markov chain can achieve uniform distribution. This modification, however, may make the sampler stay in the same node for several times, leading to undersampling. To address this issue, we propose a sampling framework that only need current and candidate node degree to improve the performance of graph sampling methods. We also extend our original idea to a more general framework. Our extended IDRW method finds a balance between the large deviation problem of SRW and sample rejection problem in MHRW. We evaluate our technique in simulation by running extensive experiments on various real-world datasets, and the result show that our method improves the accuracy compared with the state of art techniques. We also investigate the effect of the parameter and give the suggested range for a better usage in application.