一类具有分形和小世界特性的网络图  

A Class of Graphs with Fractality and Small-world Effect

作　　者：那日萨[1] 张书超[1] 穆青[2] 

机构地区：[1]大连理工大学系统工程研究所,辽宁大连116023 [2]大连理工大学数学系,辽宁大连116024

出　　处：《系统工程》2007年第3期115-119,共5页Systems Engineering

摘　　要：提出一类具有分形和小世界特性的网络图。利用数学归纳的方法计算出了网络图的集聚系数,平均最短路径和网络图的直径,证明了网络图的小世界特性。用盒维数和豪斯道夫维数来衡量网络图的分形性,得到其维数均为1.585。最后对网络图的构造方法作了进一步地拓展,并给出了拓展的网络图的相关拓扑特性的表达式,并认为其和原来的网络图可归结为一类具有分形和小世界特性的网络图。In this paper, we propose a class of graphs with fractality and small-world effect. The clustering coefficient, the average length of the graphs, and the diameter are calculated analytically. Also we calculate the box-counting dimension and Hausdorff dimension as a measure of their fractality and the value of the dimension is 1. 585. At last, the method of the constructing graphs is expanded, and the expressions of the relevant characteristics of the expanded graphs are given. The expanded graphs and the graphs proposed before are considered as a class of graphs with fractality and small-world effect.

关 键 词：复杂网络 分形 小世界 复杂系统 

分 类 号：N94[自然科学总论—系统科学] O173[理学—数学]