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Average path length of a special class of hierarchical networks
  • Jia-bao Liu,
  • Ya-Qian Zheng,
  • Kang Wang
Jia-bao Liu
Anhui Xinhua University

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Ya-Qian Zheng
Anhui Jianzhu University
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Kang Wang
Anhui Jianzhu University South Campus
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Abstract

Many of the behaviors observed in actual systems are comparable to scale-free and small world structures in network research. In contrast to conventional hierarchical networks, the unusual fractal hierarchical network we created in this research has a pyramidal structure. The findings we get from this network are expanded to be applicable to arbitrary hierarchical networks. The average path length of unweighted and weighted hierarchical networks are the main topics of this paper. We demonstrate that, in the unweighted case, when the number of iterations z tends to infinity, the average path length is only related to the number of blocks of the hierarchical network. Additionally, in the weighted network, the average path length is related to the number of blocks r and the weighting factor w of the hierarchical network.