计算机科学 ›› 2021, Vol. 48 ›› Issue (3): 136-143.doi: 10.11896/jsjkx.200700159
刘胜久, 李天瑞, 谢鹏, 刘佳
LIU Sheng-jiu, LI Tian-rui, XIE Peng, LIU Jia
摘要: 分形维数及多重分形是分形理论的重要研究内容。复杂网络的多重分形已经得到了较为深入的研究,但对复杂网络多重分形的度量目前并没有可行的方法。带权图是复杂网络研究的重要对象,其中的节点权重及边权重可以为正实数、负实数、纯虚数及复数等多种不同的类型。除节点权重及边权重均为正实数的情形外,其他类型的带权图都具有多重分形特性,且均具有无穷多个复数形式的网络维数。通过对带权图多重分形的研究,文中给出了15种具有多重分形特性的带权图多重分形维数的模所构成的集合,并采用集合的势对带权图的多重分形特性进行度量。研究表明,15种带权图多重分形维数的模所构成的集合均是可数集,其中有2种集合是2重集合,另外13种集合是通常意义上的集合,而且所有的集合均是等势的,其势均为0。
中图分类号:
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