论文标题
结构特性和直径最小的无尺度图上的平均敲击时间
Structural properties and average tapping time on scale-free graphs with smallest diameter
论文作者
论文摘要
在本文中，我们提出了一类图形$ g^{\ star}（m，t）$，并首先研究了一些结构属性，例如平均程度等。 The results show that (1) graphs $G^{\star}(m,t)$ have density feature because of their average degrees proportional to time step $t$ not to a constant in the large graph size limit, (2) graphs $G^{\star}(m,t)$ obey the power-law distribution with exponent equal to $2$, which is rarely found in most previous scale-free models, (3) graphs $ g^{\ star}（m，t）$以超小直径和较高的聚类系数显示小世界属性，以及（4）图$ g^{\ star}（m，t）$具有相对于皮尔森相关系数小于零的pearson相关系数具有损坏结构。此外，我们考虑了所提出的图表上的陷阱问题$ g^{\ star}（m，t）$，然后发现它们都通过自己的平均陷阱时间来实现理论下限的平均捕获时间，这是在现有无标度模型中很少观察到的现象。我们进行了与理论分析一致的广泛模拟。
In this paper, we propose a class of graphs $G^{\star}(m,t)$ and first study some structural properties, such as, average degree, on them. The results show that (1) graphs $G^{\star}(m,t)$ have density feature because of their average degrees proportional to time step $t$ not to a constant in the large graph size limit, (2) graphs $G^{\star}(m,t)$ obey the power-law distribution with exponent equal to $2$, which is rarely found in most previous scale-free models, (3) graphs $G^{\star}(m,t)$ display small-world property in terms of ultra-small diameter and higher clustering coefficient, and (4) graphs $G^{\star}(m,t)$ possess disassortative structure with respect to Pearson correlation coefficient smaller than zero. In addition, we consider the trapping problem on the proposed graphs $G^{\star}(m,t)$ and then find that they all have more optimal trapping efficiency by means of their own average trapping time achieving the theoretical lower bound, a phenomenon that is seldom observed in existing scale-free models. We conduct extensive simulations that are consistent with our theoretical analysis.
