递归加权科赫网络中平均的齐次与非齐次加权接收时间（英文）
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摘要
本文介绍用递归分割方法得到的实数系统上递归的齐次和非齐次的加权科赫网络模型,其主要是受机场网络和代谢网络的经验观测的启发.其中对于齐次模型,它依赖比例因子t∈(0,1);对非齐次的模型,我们通常取不同的比例因子t,s或t,r,s∈(0,1).作为基本的动力学过程,我们研究递归的齐次与非齐次的加权科赫网络的随机行走,即每一步后都将一致移动到任意一个其位于边界L_l,l=0,1,...,m,上的邻域Γ(j)中.为了更方便研究齐次与非齐次模型,我们会再次用到递归分割法以及奇异值分解法来计算所有的节点与目标节点之间最长路径的平均加权(MWLP)的总和,其中目标节点是合并节点{p_i:i=1, 2, 3}中的某个节点.最终,在庞大的网络中,平均的齐次与非齐次加权接收时间将关于网络秩序次线性.
In this paper, we introduce the recursive homogeneous weighted Koch network model for real systems with a scaling factor t ∈(0,1) and the non-homogeneous model with scaling factors t,s ∈(0,1) or t, r, s ∈(0,1). These models were constructed using the recursive division method and motivated by experimental study of aviation networks and metabolic networks. As a process of fundamental dynamics, we study the recursive homogeneous and non-homogeneous weighted Koch networks with a random walk; for all steps, the walker who is starting from an existing node moves uniformly to one of its nearest neighbors Γ(j) lying on the layers L_l,l= 0,1, · · ·,m. In order to study homogeneous and non-homogeneous models, the recursive division method and singular value decomposition were used to calculate the sum of the mean weighted longest paths(MWLP) for all nodes absorbed at the target node placed in one of the merging nodes {pi : i = 1, 2, 3}. Finally, in a large network, the average weighted receiving time(AWRT) for homogeneous and nonhomogeneous models grows sub-linearly with the network's order.
In this paper, we introduce the recursive homogeneous weighted Koch network model for real systems with a scaling factor t ∈(0,1) and the non-homogeneous model with scaling factors t,s ∈(0,1) or t, r, s ∈(0,1). These models were constructed using the recursive division method and motivated by experimental study of aviation networks and metabolic networks. As a process of fundamental dynamics, we study the recursive homogeneous and non-homogeneous weighted Koch networks with a random walk; for all steps, the walker who is starting from an existing node moves uniformly to one of its nearest neighbors Γ(j) lying on the layers L_l,l= 0,1, · · ·,m. In order to study homogeneous and non-homogeneous models, the recursive division method and singular value decomposition were used to calculate the sum of the mean weighted longest paths(MWLP) for all nodes absorbed at the target node placed in one of the merging nodes {pi : i = 1, 2, 3}. Finally, in a large network, the average weighted receiving time(AWRT) for homogeneous and nonhomogeneous models grows sub-linearly with the network's order.
引文
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[13] ZHANG Z, GAO S. Scaling of mean first-passage time as efficiency measure of nodes sending information on scale-free Koch networks[J]. The European Physical Journal B, 2011, 80(2):209-216.
[14] DAI M F, XIE Q, XI L F. Trapping on weighted tetrahedron Koch networks with small-world property[J].Fractals, 2014, 22(1/2):1450006(9 pages).
[15] SUN W. Random walks on generalized Koch networks[J]. Physica Scripta, 2013, 88(4):045006.
[16] DAI M F, YE D D, LI X Y, et al. Average weighted receiving time in recursive weighted Koch networks[J].Pramana, 2016, 86(6):1173-1182.
[17] DAI M F, LI X Y, XI L F. Random walks on non-homogenous weighted Koch networks[J]. Chaos:An Interdisciplinary Journal of Nonlinear Science, 2013, 23(3):033106.
[18] DONG Y, DAI M, YE D. Non-homogeneous fractal hierarchical weighted networks[J]. Plos One, 2015, 10(4):e0121946.
[2] CIEPLAK M, GIACOMETTI A, MARITAN A, et al. Models of fractal river basins[J]. Journal of Statistical Physics, 1998, 91(1/2):1-15.
[3] ZHAO L, LAI Y C, PARK K, et al. Onset of traffic congestion in complex networks[J]. Phys Rev E Stat Nonlin Soft Matter Phys, 2005, 71(2):026125.
[4] GARIASCHELLI D, LOFFREDO M I. Fitness-dependent topological properties of the world trade web[J].Physical Review Letters, 2004, 93(18):188701.
[5] GUIMERA R, AMARAL LAN. Modeling the world-wide airport network[J]. European Physical Journal B,2004, 38(2):381-385.
[6] MACDONALD P J, ALMAAS E, BARABASI A L. Minimum spanning trees of weighted scale-free networks[J].Epl, 2005, 72(2):308-314.
[7] DAI M, SUN Y, SHAO S, et al. Modified box dimension and average weighted receiving time on the weighted fractal networks[J]. Scientific Reports, 2015, 5:18210.
[8] WEI D J, LIU Q, ZHANG H X, et al. Box-covering algorithm for fractal dimension of weighted networks[J].Sci Rep, 2013, 3(6157):3049.
[9] CARLETTI T. Stochastic weighted fractal networks[J]. Physics, 2012, 389(10):2134-2142.
[10] CARLETTI T, RIGHI S. Weighted fractal networks[J]. Physica A, 2009, 389(10):2134-2142.
[11] YUAN Z J, GANG S W, RONG C G. Exact scaling for the mean first-passage time of random walks on a generalized Koch network with a trap[J]. Chinese Physics B, 2012, 21(3):525-529.
[12] LI L, SUN W G, WANG G X, et al. Mean first-passage time on a family of small-world treelike networks[J].International Journal of Modern Physics C, 2014, 25(3):1350097(10 pages).
[13] ZHANG Z, GAO S. Scaling of mean first-passage time as efficiency measure of nodes sending information on scale-free Koch networks[J]. The European Physical Journal B, 2011, 80(2):209-216.
[14] DAI M F, XIE Q, XI L F. Trapping on weighted tetrahedron Koch networks with small-world property[J].Fractals, 2014, 22(1/2):1450006(9 pages).
[15] SUN W. Random walks on generalized Koch networks[J]. Physica Scripta, 2013, 88(4):045006.
[16] DAI M F, YE D D, LI X Y, et al. Average weighted receiving time in recursive weighted Koch networks[J].Pramana, 2016, 86(6):1173-1182.
[17] DAI M F, LI X Y, XI L F. Random walks on non-homogenous weighted Koch networks[J]. Chaos:An Interdisciplinary Journal of Nonlinear Science, 2013, 23(3):033106.
[18] DONG Y, DAI M, YE D. Non-homogeneous fractal hierarchical weighted networks[J]. Plos One, 2015, 10(4):e0121946.