复杂网络在双曲空间的节点动态择优路径研究
|
摘要
本文研究复杂网络双曲嵌套模型.利用改进克林伯格和克莱尔科夫网络拓扑模型的方法,得到了复杂网络在双曲空间的动态择优路径,推广和发展了复杂网络节点间最优路径的算法.
In this paper, the hyperbolic nested model of complex networks is studied.By using the method of improving the topology model of Klingberg and Kellikov networks, the dynamic optimal path of complex networks in hyperbolic space is obtained, and the algorithm of optimal path between nodes of complex networks is extended and developed.
In this paper, the hyperbolic nested model of complex networks is studied.By using the method of improving the topology model of Klingberg and Kellikov networks, the dynamic optimal path of complex networks in hyperbolic space is obtained, and the algorithm of optimal path between nodes of complex networks is extended and developed.
引文
[1]胡耀光,王圣军,金涛.度关联无标度网络上的有倾向随机行走[J].物理学报, 2015, 2:28901–028901.
[2]王延,郑志刚.无标度网络上的传播动力学[J].物理学报, 2009, 58(7):4421–4425.
[3]舒盼盼,王伟,唐明.花簇分形无标度网络中节点影响力的区分度[J].物理学报, 2015, 64(20):441–451.
[4]李涛,裴文江,王少平.无标度复杂网络负载传输优化策略[J].物理学报, 2009, 58(9):5903–5910.
[5]何敏华,张端明,王海艳.基于无标度网络拓扑结构变化的舆论演化模型[J].物理学报, 2010, 59(8):5175–5181.
[6]王丹,郝彬彬.一类高聚类系数的加权无标度网络及其同步能力分析[J].物理学报, 2013, 22:69–76.
[7]柯婷婷.稀疏复杂网络的识别[J].数学杂志, 2015, 4:763–772.
[8]赵军产,李钦.复杂动力网络的鲁棒性同步[J].数学杂志, 2016, 4:727–736.
[9] Feller W. An introduction to probability theory and its applications(3rd ed.)[M]. New York:Wiley,1969.
[10]钟晓雯.动态无标度网络的演化博弈研究[D].广州:暨南大学, 2015.
[11]王延,郑志刚.无标度网络上的传播动力学[J].物理学报, 2009, 58(7):4421–4425.
[12] Kleinberg J M. Navigation in a small world[J]. Nature, 2000, 406(6798):358–359.
[13] Kleinberg J. Complex networks and decentralized search algorithms[J]. Inter. Cong. Math., 2007:1019–1044.
[14] Kleinberg J M, Kumar R, Raghavan P. The web as a graph:measurements, models, and methods[J].Intern. Conf. Comp. Comb., Springer-Verlag, 1999:1–17.
[15] Krioukov D, Papadopoulos F, Vahdat A. Hyperbolic geometry of complex networks[J]. Phys. Rev.E Stat. Nonl. Soft Matt. Phys., 2010, 82(3 Pt 2):98–118.
[16] Krioukov D, Papadopoulos F, Bogu?n′a M. Greedy forwarding in dynamic scale-free networks embedded in hyperbolic metric spaces[J]. ACM Sigm. Perf. Eval. Rev., 2009, 37(2):15–17.
[17] Krioukov D, Papadopoulos F, Bogun′a M. Efficient navigation in scale-free networks embedded in hyperbolic metric spaces[J]. Eprint Arxiv, 2008, 54(1):1–9.
[18] Krapivsky P, Krioukov D. Scale-free networks as preasymptotic regimes of superlinear preferential attachment[J]. Phys. Rev. E, 2008, 78(2):1–11.
[19] Serrano M A, Krioukov D, Bogun′a M. Self-similarity of complex networks and hidden metric spaces[J]. Phys. Rev. Lett., 2008, 100(7):652–663.
[20] Aldecoa R, Orsini C, Krioukov D. Hyperbolic graph generator[J]. Comp. Phys. Commun., 2015,196:492–496.
[2]王延,郑志刚.无标度网络上的传播动力学[J].物理学报, 2009, 58(7):4421–4425.
[3]舒盼盼,王伟,唐明.花簇分形无标度网络中节点影响力的区分度[J].物理学报, 2015, 64(20):441–451.
[4]李涛,裴文江,王少平.无标度复杂网络负载传输优化策略[J].物理学报, 2009, 58(9):5903–5910.
[5]何敏华,张端明,王海艳.基于无标度网络拓扑结构变化的舆论演化模型[J].物理学报, 2010, 59(8):5175–5181.
[6]王丹,郝彬彬.一类高聚类系数的加权无标度网络及其同步能力分析[J].物理学报, 2013, 22:69–76.
[7]柯婷婷.稀疏复杂网络的识别[J].数学杂志, 2015, 4:763–772.
[8]赵军产,李钦.复杂动力网络的鲁棒性同步[J].数学杂志, 2016, 4:727–736.
[9] Feller W. An introduction to probability theory and its applications(3rd ed.)[M]. New York:Wiley,1969.
[10]钟晓雯.动态无标度网络的演化博弈研究[D].广州:暨南大学, 2015.
[11]王延,郑志刚.无标度网络上的传播动力学[J].物理学报, 2009, 58(7):4421–4425.
[12] Kleinberg J M. Navigation in a small world[J]. Nature, 2000, 406(6798):358–359.
[13] Kleinberg J. Complex networks and decentralized search algorithms[J]. Inter. Cong. Math., 2007:1019–1044.
[14] Kleinberg J M, Kumar R, Raghavan P. The web as a graph:measurements, models, and methods[J].Intern. Conf. Comp. Comb., Springer-Verlag, 1999:1–17.
[15] Krioukov D, Papadopoulos F, Vahdat A. Hyperbolic geometry of complex networks[J]. Phys. Rev.E Stat. Nonl. Soft Matt. Phys., 2010, 82(3 Pt 2):98–118.
[16] Krioukov D, Papadopoulos F, Bogu?n′a M. Greedy forwarding in dynamic scale-free networks embedded in hyperbolic metric spaces[J]. ACM Sigm. Perf. Eval. Rev., 2009, 37(2):15–17.
[17] Krioukov D, Papadopoulos F, Bogun′a M. Efficient navigation in scale-free networks embedded in hyperbolic metric spaces[J]. Eprint Arxiv, 2008, 54(1):1–9.
[18] Krapivsky P, Krioukov D. Scale-free networks as preasymptotic regimes of superlinear preferential attachment[J]. Phys. Rev. E, 2008, 78(2):1–11.
[19] Serrano M A, Krioukov D, Bogun′a M. Self-similarity of complex networks and hidden metric spaces[J]. Phys. Rev. Lett., 2008, 100(7):652–663.
[20] Aldecoa R, Orsini C, Krioukov D. Hyperbolic graph generator[J]. Comp. Phys. Commun., 2015,196:492–496.