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首页> 外文期刊>Physica, A. Statistical mechanics and its applications >Detecting unknown paths on complex networks through random walks
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Detecting unknown paths on complex networks through random walks

机译：通过随机游走检测复杂网络上的未知路径

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In this article, we investigate the problem of detecting unknown paths on complex networks through random walks. To detect a given path on a network a random walker should pass through the path from its initial node to its terminal node in turn. We calculate probability phi(t) that a random walker detects a given path on a connected network in t steps when it starts out from source node s. We propose an iteration formula for calculating phi(t). Generating function of phi(t) is also derived. Major factors affecting phi(t), such as walking time t, path length l, starting point of the walker, structure of the path, and topological structure of the underlying network are further discussed. Among these factors, two most outstanding ones are walking time t and path length l. On the one hand, (t) increases as t increases, and phi(infinity) = 1, which shows that the longer the walking time, the higher the chance of detecting a given path, and the walker will discover the path sooner or later so long as it keeps wandering on the network. On the other hand, phi(t) drops substantially as path length 1 increases, which shows that the longer the path, the lower the chance for the walker to find it in a given time. Apart from path length, path structure also has obvious effect on phi(t). Starting point of the walker has only minor influence on phi(t), but topological structure of the underlying network has strong influence on phi(t). Simulations confirm our analytic results.
机译：在本文中，我们研究了通过随机游走检测复杂网络上未知路径的问题。为了检测网络上的给定路径，随机步行者应依次通过从其初始节点到其终端节点的路径。我们计算出当随机行者从源节点s开始时，它会在t步中以t步检测到随机路径的概率phi（t）。我们提出一个迭代公式来计算phi（t）。还推导了phi（t）的生成函数。进一步讨论了影响phi（t）的主要因素，例如步行时间t，路径长度l，步行者的起点，路径结构以及基础网络的拓扑结构。在这些因素中，两个最突出的因素是步行时间t和路径长度l。一方面，（t）随着t的增加而增加，并且phi（infinity）= 1，这表明步行时间越长，检测到给定路径的机会就越高，步行者迟早会发现该路径。只要它一直在网络上徘徊。另一方面，phi（t）随路径长度1的增加而大幅下降，这表明路径越长，步行者在给定时间内找到它的机会就越小。除路径长度外，路径结构对phi（t）也有明显影响。步行者的起点对phi（t）的影响很小，但是基础网络的拓扑结构对phi（t）的影响很大。仿真证实了我们的分析结果。

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