具有记忆的时变网络中的随机游动
Random walks in time-varying networks with memory
摘要：
网络中的随机游走过程在理解节点的重要性和相似性方面起着基础性的作用，在PageRank、信息检索、社区检测等方面有着广泛的应用。个体的记忆被证明是影响网络演化和网络动态过程的重要因素。在本文中，我们研究了扩展的活动驱动网络模型上的随机行走过程，该模型考虑了个体的记忆。我们分析了当随机游走过程和网络演化的时间尺度相当时，个体记忆如何影响网络上随机游走过程的展开。在长时间演化的约束下，我们得到了定态分布Wa和随机行走过程的平均首次通过时间（MFPT）的解析解。我们发现，与无记忆活动驱动模型相比，个体记忆增强了度分布的波动性，降低了节点聚集步行者的能力，特别是在大活动的情况下，并延迟了平均首次通过时间。真实网络上的结果也支持了人工网络的理论分析。
英文摘要：
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. Individual's memory has been proved to be important to affect network evolution and dynamical processes unfolding on the network. In this manuscript, we study the random-walk process on extended activity driven network model by taking account of individual's memory. We analyze how 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 stationary state Wa and the mean first-passage time (MFPT) of the random-walk process. We find that, compared with the memoryless activity-driven model, individual's memory enhances the fluctuation of degree distribution, which reduces the capability of gathering walkers for nodes, especially with large activity and delays the mean first-passage time. The results on real networks also support the theoretical analysis with artificial networks.
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