多重网络上的Levy随机游动
Levy random walks on multiplex networks
摘要：
随机游走是复杂网络中许多动力学行为的基本机制。此外，作为一个更现实的描述我们的社会，多元化网络已经收到越来越多的兴趣，以及动态过程发生在他们之上。在这里，灵感来自一个特定的模型的随机游走，似乎是无处不在的许多科学领域，利维飞行，我们研究了一个新的导航策略上的多重网络。利用谱图和随机矩阵理论，我们推导出平均首次通过时间和平均时间到达这些网络上的节点的解析表达式。此外，我们还探讨了Levy随机游走的效率，我们发现与单层场景相比，Levy随机游走的效率非常不同，这是由于多重网络固有的结构和动力学。最后，通过与多重网络上其他一些重要的随机游动过程的比较，我们发现在某些参数范围内，Levy随机游动是最有效的策略。我们的研究结果给了我们一个更深层次的理解利维随机游动，并显示出的重要性，考虑多重网络的拓扑结构时，试图找到有效的导航策略。
英文摘要：
Random walks constitute a fundamental mechanism for many dynamics taking place on complex networks. Besides, as a more realistic description of our society, multiplex networks have been receiving a growing interest, as well as the dynamical processes that occur on top of them. Here, inspired by one specific model of random walks that seems to be ubiquitous across many scientific fields, the Levy flight, we study a new navigation strategy on top of multiplex networks. Capitalizing on spectral graph and stochastic matrix theories, we derive analytical expressions for the mean first passage time and the average time to reach a node on these networks. Moreover, we also explore the efficiency of Levy random walks, which we found to be very different as compared to the single layer scenario, accounting for the structure and dynamics inherent to the multiplex network. Finally, by comparing with some other important random walk processes defined on multiplex networks, we find that in some region of the parameters, a Levy random walk is the most efficient strategy. Our results give us a deeper understanding of Levy random walks and show the importance of considering the topological structure of multiplex networks when trying to find efficient navigation strategies.
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