基于向量空间的多子网复合复杂网络模型动态组网运算的形式描述

Formalized Descriptions of Dynamic Reorganizations of Multi-Subnet Composited Complex Network Based on Vector Space

针对典型复杂网络模型仅描述了复杂系统中同一类个体及其间一种相互关系且对问题的讨论仅局限于同一个系统的问题,基于能够描述复杂系统中异类个体间多种关系的多子网复合复杂网络模型,导入多维向量空间,将网络节点间的关系映射为多维向量,定义了向量复合网.在此基础上,将该模型的动态组网运算(加载与退缩)转化为向量空间的基变换,给出了加载运算与退缩运算的形式描述,实现了多子网复合复杂网络的可计算.建立并分析了我国铁路客运复合网,通过网络动态重组运算,基于高速铁路子网与低速铁路子网的拓扑性质,给出了我国铁路发展现状分析.

Classical complex networks mainly describe same type of entities and one type of interrelations between the entities. Multi-subnet composited network is a model that describes different types of entities and multiple types of interrelations between the entities. Dynamic reorganization of this model provide two operations： Compounding （combine two subnets into a ＂bigger＇ one） and reducing （obtain a ＇small＇ network from a ＇big＇ one）. In this paper, a vector-composited network is defined by importing multi-dimensional space, which converts the.interrelations between entities into multi-dimensional vector. Dynamic reorganization of networks is converted into base transformations in multi-dimensional space. Formalized descriptions of compounding and reducing are presented. Further, vector-composited network of passenger transport with high speed and low speed railways in China's Mainland is established by empirical data. Topological analysis of networks obtained by dynamic reorganizations illustrates the development of railway system in China's Mainland.