Dai, Mei-Feng; Ju, Ting-Ting; Hou, Yong-Bo; Huang, Fang; Tang, Dong-Lei; Su, Wei-Yi Applications of Markov spectra for the weighted partition network by the substitution rule. (English) Zbl 1451.05216 Commun. Theor. Phys. 72, No. 5, Article ID 055602, 8 p. (2020). Summary: The weighted self-similar network is introduced in an iterative way. In order to understand the topological properties of the self-similar network, we have done a lot of research in this field. Firstly, according to the symmetry feature of the self-similar network, we deduce the recursive relationship of its eigenvalues at two successive generations of the transition-weighted matrix. Then, we obtain eigenvalues of the Laplacian matrix from these two successive generations. Finally, we calculate an accurate expression for the eigentime identity and Kirchhoff index from the spectrum of the Laplacian matrix. Cited in 1 Document MSC: 05C82 Small world graphs, complex networks (graph-theoretic aspects) 05C85 Graph algorithms (graph-theoretic aspects) Keywords:weighted self-similar network; Laplacian matrix; eigentime identity; Kirchhoff index; substitution rule PDFBibTeX XMLCite \textit{M.-F. Dai} et al., Commun. Theor. Phys. 72, No. 5, Article ID 055602, 8 p. (2020; Zbl 1451.05216) Full Text: DOI References: [1] Albert R and Barabsi A 2002 Rev. Mod. Phys.74 47 · Zbl 1205.82086 [2] Newman M 2003 Siam. Rev.45 167-256 · Zbl 1029.68010 [3] Albert R, Jeong H and Barabasi A 2000 Nature340 378-82 [4] Rubinov M and Sporns O 2010 NeuroImage52 1059-69 [5] Motter A, Zhou C and Kurths J 2004 Vaccine22 1820-5 [6] Chen Y F, Dai M F and Wang X Q 2018 Fractals26 1850017 · Zbl 1432.35058 [7] Dai M F, Wang X Q and Zong Y 2017 Fractals25 1750049 · Zbl 1421.05083 [8] Kuperman M and Abramson G 2001 Phys. Rev. Lett.86 2909-12 [9] Fronczak A and Fronczak P 2004 Phys. Rev. E 70 056110 [10] Zhang P, Wang J and Li X 2012 Physica A 387 6869-75 [11] Barthlemy M 2004 Eur. Phys. J. B 38 163-8 [12] Cowley M, Smart J and Rubinstein M 2001 Nature411 480-4 [13] Albert R, Jeong H and Barabsi A 1999 Nature401 130-1 [14] Yang H and Huang H J 2004 Transport. Res. Part. B 38 1-15 [15] Bolton P and Dewatripont M 1994 Q. J. Econ109 809-39 · Zbl 0826.90072 [16] Lee C, Loh P S and Sudakov B 2013 Siam. J. Discrete. Math.27 959-72 · Zbl 1272.05087 [17] Qi Z H, Li L and Zhang Z M 2011 J. Theor. Biol.280 10-8 · Zbl 1397.92227 [18] Dai M F, Ju T T and Liu J Y 2018 Int. J. Mod. Phys. B 32 1850353 · Zbl 1423.93045 [19] Dai M F, Wang X Q and Chen Y F 2018 Physica A 505 1-8 [20] Dai M F, He J J and Zong Y 2018 Chaos28 043110 · Zbl 1392.37043 [21] Xie P, Zhang Z Z and Comellas F 2015 Appl. Math. Comput273 1123-9 · Zbl 1410.05143 [22] Julaiti A, Wu B and Zhang Z 2013 J. Chem. Phys.138 204116 [23] Jia Q and Tang W 2017 IEEE Trans. Circuits Syst. I 65 723-32 [24] Jia Q and Tang W 2018 IEEE Trans. Circuits Syst. II 65 1969-73 [25] Li H B, Huang T Z and Shen S Q 2007 Linear. Algebra. Appl.420 235-47 · Zbl 1172.15008 [26] Pucci C 1966 Proc. Am. Math. Soc.17 788-95 [27] Xia S C and Xi L F 2004 Chin. J. Mech. Eng.11 405-10 [28] Dai M F, Tang H L and Zou J H 2017 Int. J. Mod. Phys. B 32 1850021 · Zbl 1429.05122 [29] Shan L, Li H and Zhang Z 2017 Theor. Comput. Sci.677 12-30 · Zbl 1369.05164 [30] Chen H and Zhang F 2007 Discrete. Appl. Math.155 654-61 · Zbl 1113.05062 [31] Mao Y 2004 J. Appl. Probab41 1071-80 [32] Gao X, Luo Y and Liu W 2012 Discrete. Appl. Math.160 560-5 · Zbl 1239.05053 [33] Li T T, Xi L F and Ye Q Q 2018 Fractals26 1850064 · Zbl 1433.35441 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.