Wang Bing, Zeng Hongjuan, Han Yuexing
School of Computer Engineering and Science, Shanghai University, Shanghai, P.R. China.
Shanghai Institute for Advanced Communication and Data Science, Shanghai University, Shanghai, P.R. China.
Phys Rev E. 2020 Dec;102(6-1):062309. doi: 10.1103/PhysRevE.102.062309.
Random walks process on networks plays a fundamental role in understanding the importance of nodes and the similarity of them, which has been widely applied in PageRank, information retrieval, and community detection, etc. An individual's memory has been proved to be crucial to affect network evolution and dynamical processes unfolding on the network. In this work, we study the random-walk process on an extended activity-driven network model by taking account of an individual's memory. We analyze how an individual's memory affects random-walk process unfolding on the network when the timescales of the processes of the random walk and the network evolution are comparable. Under the constraints of long-time evolution, we derive analytical solutions for the distribution of walkers at the stationary state and the mean first-passage time of the random-walk process. We find that, compared with the memoryless activity-driven model, an individual's memory enhances the activity fluctuation and leads to the formation of small clusters of mutual contacts with high activity nodes, which reduces a node's capability of gathering walkers, especially for the nodes with large activity, and memory also delays the mean first-passage time. The results on real networks also support the theoretical analysis and numerical results with artificial networks.
网络上的随机游走过程在理解节点的重要性及其相似性方面起着基础性作用，已广泛应用于网页排名、信息检索和社区检测等领域。个体记忆已被证明对影响网络演化以及网络上展开的动态过程至关重要。在这项工作中，我们通过考虑个体记忆来研究扩展的活动驱动网络模型上的随机游走过程。当随机游走过程和网络演化过程的时间尺度可比时，我们分析个体记忆如何影响在网络上展开的随机游走过程。在长时间演化的约束下，我们推导了平稳状态下游行者分布和随机游走过程平均首次通过时间的解析解。我们发现，与无记忆活动驱动模型相比，个体记忆增强了活动波动，并导致形成与高活动节点相互接触的小集群，这降低了节点聚集游走者的能力，特别是对于具有大活动量的节点，并且记忆还会延迟平均首次通过时间。真实网络上的结果也支持人工网络的理论分析和数值结果。
