论文标题
根据两个新型分形网络模型研究分形的起源
Investigating the Origins of Fractality Based on Two Novel Fractal Network Models
论文作者
论文摘要
已经研究了许多网络模型，以了解分形的起源。在这项工作中，我们介绍了两个新型的网络模型，以更好地了解分形网络的增长机制和结构特征。基于排斥的分形模型（RBFM）是建立在著名的歌曲 - 哈夫林 - 麦克斯（SHM）模型上的，但在RBFM中，在特定的节点组中始终存在。该模型通过表明排斥是诱导分形的特征来解决SHM模型与集线器吸引动力学生长模型之间的矛盾。晶格小世界过渡模型（LSWTM）的动机是由排斥直接影响节点距离的事实。通过LSWTM，我们研究了分形小世界的过渡。该模型说明了使用基于优先连接的边缘重新布线的过程对固定数量的节点和边缘上的过渡。它表明，平均距离较小，与分形尺度相对，并且还表明分形不是二分法特性，可以在纯分形和非骨骼特性之间观察到连续的过渡。
Numerous network models have been investigated to gain insights into the origins of fractality. In this work, we introduce two novel network models, to better understand the growing mechanism and structural characteristics of fractal networks. The Repulsion Based Fractal Model (RBFM) is built on the well-known Song-Havlin-Makse (SHM) model, but in RBFM repulsion is always present among a specific group of nodes. The model resolves the contradiction between the SHM model and the Hub Attraction Dynamical Growth model, by showing that repulsion is the characteristic that induces fractality. The Lattice Small-world Transition Model (LSwTM) was motivated by the fact that repulsion directly influences the node distances. Through LSwTM we study the fractal-small-world transition. The model illustrates the transition on a fixed number of nodes and edges using a preferential-attachment-based edge rewiring process. It shows that a small average distance works against fractal scaling, and also demonstrates that fractality is not a dichotomous property, continuous transition can be observed between the pure fractal and non-fractal characteristics.
