Ma Fei, Wang Ping
School of Electronics Engineering and Computer Science, Peking University, Beijing 100871, China.
National Engineering Research Center for Software Engineering, Peking University, Beijing 100871, China.
Phys Rev E. 2021 Feb;103(2-1):022318. doi: 10.1103/PhysRevE.103.022318.
Here, we propose a simple algorithmic framework for creating power-law graphs with small diameters and then study structural properties, for instance, average degree, on graphs built. The results show that our graphs have not only some commonly seen properties including scale-free feature, small-world property, and disassortative structure, but also many rarely found characteristics, such as the density feature due to power-law exponents equal to 2 and the diameter equivalent to 2, compared to most previous scale-free models. In addition, we also consider the trapping problem on the proposed graphs and then find that they have more optimal trapping efficiency by means of their own average trapping times achieving the theoretical lower bound, a phenomenon that is seldom observed in existing scale-free models. We conduct extensive simulations, and the results show that empirical simulations are consistent with theoretical analysis.
在此，我们提出了一个用于创建具有小直径的幂律图的简单算法框架，然后研究构建的图的结构特性，例如平均度。结果表明，我们的图不仅具有一些常见特性，包括无标度特征、小世界特性和异配结构，而且与大多数先前的无标度模型相比，还有许多罕见的特征，例如幂律指数等于2时的密度特征以及直径等于2。此外，我们还考虑了所提出的图上的捕获问题，然后发现它们通过自身的平均捕获时间达到理论下限而具有更高的最优捕获效率，这一现象在现有无标度模型中很少观察到。我们进行了广泛的模拟，结果表明实证模拟与理论分析一致。
