Weighted Jump in Random Walk Graph Sampling

Random walk based 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 GMD modify the topology of target graphs so that the long-term behavior of Markov chain can achieve uniform distribution. This modification, however, reduces the conductance of graphs, thus makes the sampler stay in the same node for long time, resulting in undersampling. To address this issue, we propose a new way of modifying target graph, thus propose Weighted Jump Random Walk (WJRW) with parameter C to improve the performance. We prove that WJRW can unify Simple Random Walk and uniform distribution through C, and we also conduct extensive experiments on real-world dataset. The experimental results show WJRW can promote the accuracy significantly under the same budget. We also investigate the effect of the parameter C, and give the suggested range for a better usage in application.