论文标题
多路复用网络上的非平衡随机步行
Non-equilibrium random walks on multiplex networks
论文作者
论文摘要
我们在多路复用网络上引入了一个非平衡离散时间随机步行模型，在每个时间步骤中，沃克首先在同一层的相邻节点之间进行随机跳跃，然后尝试从另一个层中的一个节点跳到其一个副本。我们得出了所谓的Supra-Markov矩阵，该基质控制着沃克的职业概率的演变。除非层之间的过渡概率消失，否则平稳性的职业概率与每一层的加权平均值不同。但是，当层之间的过渡概率很小时，它们大约相等，这是由一阶退化扰动理论给出的。此外，我们计算平均第一个传递时间（MFPT）和图形MFPT（GRMFPT），这是所有对不同节点的平均值。有趣的是，我们发现GRMFPT可以小于孤立的任何层的GRMFPT。结果体现了多路复用网络上全局搜索的优势。
We introduce a non-equilibrium discrete-time random walk model on multiplex networks, in which at each time step the walker first undergoes a random jump between neighboring nodes in the same layer, and then tries to hop from one node to one of its replicas in another layer. We derive the so-called supra-Markov matrix that governs the evolution of the occupation probability of the walker. The occupation probability at stationarity is different from the weighted average over the counterparts on each layer, unless the transition probabilities between layers vanish. However, they are approximately equal when the transition probabilities between layers are very small, which is given by the first-order degenerate perturbation theory. Moreover, we compute the mean first passage time (MFPT) and the graph MFPT (GrMFPT) that is the average of the MFPT over all pairs of distinct nodes. Interestingly, we find that the GrMFPT can be smaller than that of any layer taken in isolation. The result embodies the advantage of global search on multiplex networks.
