AVERAGE FERMAT DISTANCE OF A PSEUDO-FRACTAL HIERARCHICAL SCALE-FREE NETWORK

Lulu Peng (), Cheng Zeng (), Dirong Chen (), Yumei Xue and Zixuan Zhao ()
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Lulu Peng: School of Mathematical Science, Beihang University, Beijing 100083, P. R. China
Cheng Zeng: School of Mathematical Science, Beihang University, Beijing 100083, P. R. China
Dirong Chen: School of Mathematical Science, Beihang University, Beijing 100083, P. R. China
Yumei Xue: School of Mathematical Science, Beihang University, Beijing 100083, P. R. China
Zixuan Zhao: School of Mathematical Science, Beihang University, Beijing 100083, P. R. China

FRACTALS (fractals), 2023, vol. 31, issue 01, 1-12

Abstract: Fermat point of a triangle is the point with the minimal total distance from the three vertices in a triangle. In this paper, we discuss the average Fermat distance for a class of hierarchical networks. First, the unweighted hierarchical scale-free network is established in an iterative way. Applying the recursive method, we deduce the analytical expression of average Fermat distance and average geodesic distance. Then we reveal the linear relation of the leading terms for average Fermat distance and average geodesic distance. Finally, we obtain the small-world property of the hierarchical scale-free network, which indicates that average Fermat distance can be a valuable index of small-word property.

Keywords: Fractal; Hierarchical Network; Average Fermat Distance; Average Geodesic Distance; Small-World (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23500135

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