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The average shortest distance of three colored substitution networks

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  • Hu, Zhongren
  • Wu, Bo

Abstract

The circuit is a system composed of multiple components. The module of the circuit refers to the combination of components with similar functions in the circuit to form a module. In order to study the transmission efficiency of the circuit module, this paper projects it into three color substitution networks. The three colors are blue, red and green, respectively, representing a combination of circuit modules, based on certain substitution rules during the construction of the network. This paper studies the average shortest path between any two nodes in the circuit module, which reflects the transmission efficiency of the network. We calculate the shortest distance between the initial nodes of different modules and obtain the average shortest distance across the entire network based on the substitute iteration rules generated by the network. The results show that with the continuous expansion of the network, the average shortest distance is sub-linearly fitted to the network order.

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  • Hu, Zhongren & Wu, Bo, 2023. "The average shortest distance of three colored substitution networks," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    • Handle: RePEc:eee:chsofr:v:176:y:2023:i:c:s0960077923010081
    DOI: 10.1016/j.chaos.2023.114107
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    1. Yang, Jinling & Chen, Zhiwei & Criado, Regino & Zhang, Shenggui, 2024. "A mathematical framework for shortest path length computation in multi-layer networks with inter-edge weighting and dynamic inter-edge weighting: The case of the Beijing bus network, China," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).

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