论文标题
通过全局平均第一返回时间衡量的最佳网络
Optimal networks measured by global mean first return time
论文作者
论文摘要
随机步行在现实生活中广泛应用，从目标搜索，反应动力学，聚合物链到对极端事件，疾病或意见的到来的预测。在本文中，我们考虑在一般连接的网络上进行离散随机步行，并专注于全球平均第一个返回时间（GMFRT）的分析，该分析被定义为在所有可能的启动位置（顶点）上平均平均第一次返回时间（旨在查找具有最大（或最小）GMFRT与同一图形的最大（或最小）GMFRT图形的结构。我们的结果表明，在所有具有相同数量的顶点的树中，具有线性结构的树是具有最小GMFRT的结构，而恒星是具有最大GMFRT的结构。我们还发现，在所有具有相同数量的顶点的连接图中，其顶点具有相同程度的图是具有最小GMFRT的结构。顶点度具有最大差异的图是具有最大GMFRT的结构。我们还提供了使用最大GMFRT（或最小GMFRT）构造图形的方法，以及所有连接的图形，具有相同数量的顶点和边缘。
Random walks have wide application in real lives, ranging from target search, reaction kinetics, polymer chains, to the forecast of the arrive time of extreme events, diseases or opinions. In this paper, we consider discrete random walks on general connected networks and focus on the analysis of the global mean first return time (GMFRT), which is defined as the mean first return time averaged over all the possible starting positions (vertices), aiming at finding the structures who have the maximal (or the minimal) GMFRT among all connected graphs with the same number of vertices and edges. Our results show that, among all trees with the same number of vertices, trees with linear structure are the structures with the minimal GMFRT and stars are the structures with the maximal GMFRT. We also find that, among all connected graphs with the same number of vertices, the graphs whose vertices have the same degree, are the structures with the minimal GMFRT; and the graphs whose vertex degrees have the biggest difference, are the structures with the maximal GMFRT. We also present the methods for constructing the graphs with the maximal GMFRT (or the minimal GMFRT), among all connected graphs with the same number of vertices and edges.
