图模型上Fibonacci级数与纯优先连接机制的握手
Handshake between Fibonacci series and pure preferential attachment mechanism on a graph-model
摘要：
为了更好地理解自然界和人造复杂系统的动力学函数，统计物理、数学、理论计算机科学等多个学科的研究人员都投入了大量的精力进行这一有趣的研究。如何构造合理的图模型，并利用已有的理论模型来解释现实网络的诸多特性，仍然是本文的主要工作。与已有的确定性图模型相比，新的确定性图模型可以通过三种不同的生长方式来满足优先连接机制。同时，还介绍了几个与网络研究相关的典型指标。此外，还将展示一些有趣的发现，包括Fibonacci系列和“纯”优先连接机制之间的第一次握手，连接两个著名规则的明显关系，幂律和Zipf律，以及一个共同但有用的方程，基于生成树数和最大叶生成树数。基于上述讨论，我们可以证明我们的图模型服从幂律和小世界性质。最后，对未来的研究方向提出了一些有待进一步研究的问题。
英文摘要：
In order to better understand dynamical functions on amounts of natural and man-made complex systems, lots of researchers from a wide range of disciplines, covering statistic physics, mathematics, theoretical computer science, and so on, have spent much time in doing this intriguing study. In this paper, the discussed popularly topic, how to construct reasonable graph-model and then to explain many features of realistic networks using previously presented theoretical models, is still our main work. Compared with many pre-existing deterministic graph-model in single evolution way, our new graph-model can be constructed using three types of growth ways to meet preferential attachment mechanism. Meanwhile several typical indices associated with network research will be reported. In addition, some interesting findings will be shown, including the first handshake between Fibonacci series and "pure" preferential attachment mechanism, an obvious relationship connecting two well-known rules, power-law and Zipf-law, and a common but useful equation on the basis of both spanning trees number and the number of spanning trees with maximum leaves. Based on these foregoing discussions, we can demonstrate that our graph-model obeys power-law and small-world property. For the future research directions, we present some unknown problems to be studied at the end of this paper.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
