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Article

Mean Hitting Time for Random Walks on a Class of Sparse Networks

by 1,2,†, 1,2,*,† and 3,†
1
School of Electronics Engineering and Computer Science, Peking University, NO. 5 Yiheyuan Road, Haidian District, Beijing 100871, China
2
Key Laboratory of High Confidence Software Technologies, Peking University, Beijing 100871, China
3
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editors: Miquel Montero and Antonio Maria Scarfone
Entropy 2022, 24(1), 34; https://doi.org/10.3390/e24010034
Received: 2 November 2021 / Revised: 9 December 2021 / Accepted: 21 December 2021 / Published: 24 December 2021
(This article belongs to the Special Issue New Trends in Random Walks)
For random walks on a complex network, the configuration of a network that provides optimal or suboptimal navigation efficiency is meaningful research. It has been proven that a complete graph has the exact minimal mean hitting time, which grows linearly with the network order. In this paper, we present a class of sparse networks G(t) in view of a graphic operation, which have a similar dynamic process with the complete graph; however, their topological properties are different. We capture that G(t) has a remarkable scale-free nature that exists in most real networks and give the recursive relations of several related matrices for the studied network. According to the connections between random walks and electrical networks, three types of graph invariants are calculated, including regular Kirchhoff index, M-Kirchhoff index and A-Kirchhoff index. We derive the closed-form solutions for the mean hitting time of G(t), and our results show that the dominant scaling of which exhibits the same behavior as that of a complete graph. The result could be considered when designing networks with high navigation efficiency. View Full-Text
Keywords: complex network; graphic operation; random walk; mean hitting time; Kirchhoff index complex network; graphic operation; random walk; mean hitting time; Kirchhoff index
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MDPI and ACS Style

Su, J.; Wang, X.; Yao, B. Mean Hitting Time for Random Walks on a Class of Sparse Networks. Entropy 2022, 24, 34. https://doi.org/10.3390/e24010034

AMA Style

Su J, Wang X, Yao B. Mean Hitting Time for Random Walks on a Class of Sparse Networks. Entropy. 2022; 24(1):34. https://doi.org/10.3390/e24010034

Chicago/Turabian Style

Su, Jing, Xiaomin Wang, and Bing Yao. 2022. "Mean Hitting Time for Random Walks on a Class of Sparse Networks" Entropy 24, no. 1: 34. https://doi.org/10.3390/e24010034

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