Computer Science

Computer Science ›› 2021, Vol. 48 ›› Issue (3): 136-143.doi: 10.11896/jsjkx.200700159

• Database & Big Data & Data Science • Previous Articles     Next Articles

Measure for Multi-fractals of Weighted Graphs

LIU Sheng-jiu, LI Tian-rui, XIE Peng, LIU Jia   

  1. School of Information Science and Technology,Southwest Jiaotong University,Chengdu 611756,China
    Sichuan Key Lab of Cloud Computing and Intelligent Technique,Chengdu 611756,China
  • Received:2020-07-26 Revised:2020-08-28 Online:2021-03-15 Published:2021-03-05
  • About author:LIU Sheng-jiu,born in 1988,Ph.D,post Ph.D.His main research interests include complex network,natural language processing,data mining,etc.
    LI Tian-rui,born in 1969,Ph.D,professor,Ph.D supervisor,is a member of China Computer Federation.His main research interests include data mining and knowledge discovery,granular computing and rough sets,cloud computing and big data,etc.
  • Supported by:
    National Natural Science Foundation of China (61573292).

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Abstract: Fractal dimension and multi-fractal are important research contents of fractal theory.The multi-fractal of complex networks has been studied in depth,while there is no feasible method to measure the multi-fractal of complex networks.Weighted graph is an important research object of complex network.Both node weight and edge weight in weighted graphs can be positive real number,negative real number,pure imaginary number and complex number,and so on.Among all types of weighted graphs,except the weighted graphs with both node weight and edge weight being positive real numbers,other types of weighted graphs share multi-fractals and append with infinity complex network dimensions.Through the study of multi-fractals of weighted graphs,this paper presents modulus of infinity complex network dimensions of all 15 weighted graphs that share multi-fractal,and measures multi-fractal of them by cardinality of sets obtained from modulus of infinity complex network dimensions of them.It shows that all sets obtained from modulus of infinity complex network dimensions of weighted graphs share multi-fractal are countable sets,while 2 are multisets,and the other 13 are ordinary sets.Moreover,all sets,regardless of multisets or ordinary sets,are equipotent with cardinality of 0.

Key words: Cardinality, Complex network, Fractal dimension, Fractal theory, Measure, Multi-fractals, Weighted graph

CLC Number: 

  • TP393
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