Abstract:In order to reveal some characteristics of supernetworks,in this paper we proposed and established four kinds of three-layer network evolution models based on small-world and scale-free model, and defined two kinds of the layer intersectant degree between the levels, which are used to measure the cooperation-competition relation between network nodes. The numerical analytical results show that for the supernetwork theory model and empirical analysis, the layer intersectant degrees can not only be used to analyze the relationship between different layers of nodes, but also describe and quantify supernetwork robustness, From the theory our research results further deep perfect the multi-layered supernetwork evolution models, and lay a certain foundation for applications.
刘强, 方锦清, 李永. 三层超网络演化模型特性研究[J]. 复杂系统与复杂性科学, 2015, 12(2): 64-71.
LIU Qiang, FANG Jinqing, LI Yong. Some Characteristics of Three-Layer Supernetwork Evolution Model[J]. Complex Systems and Complexity Science, 2015, 12(2): 64-71.
[1] Watts D J, Strogatz S H. Collective dynamics of ′small-world′ networks[J]. Nature, 1998, 393: 440-442. [2] Barabási A L, Alber R. Emergence of scaling in random network[J]. Science, 1999, 286: 509-512. [3] Barabási A L, Albert R, Jeong H. Mean-field theory for scale-free random networks[J]. Phys A, 1999, 272: 173-187. [4] Newman M E J. Models of the small world[J]. J Stat Phys, 2000, 101: 819-841. [5] Fang J Q,Bi Q, Li Y, et al. Sensitivity of exponents of three-power-laws to hybrid ratio in weighted HUHPM[J]. Chi Phys Lett, 2007, 24(1):279-282. [6] Fang J Q, Bi Q, Li Y. From a harmonious unifying hybrid preferential model toward a large unifying hybrid network model[J]. International Journal of Modern Physics B, 2007, 21(30): 5121-5142. [7] 刘强,方锦清,毕桥,等. 多种形式的加权广义Farey组织网络金字塔的复杂性[J]. 物理学报, 2010, 59(6): 3704-3714. Liu Qiang, Fang Jinqing, Bi Qiao, et al. The complexity of multi-architecture type of deterministic weighted generalized Farey organized network pyramid[J]. Acta Physica Sinica, 2010, 59(6): 3704-3714. [8] 田立新, 贺莹环, 黄益. 一种新型二分网络类局域世界演化模型[J]. 物理学报, 2012: 61(22): 558-564. Tian Lixin, He Yinghuan, Huang Yi. A novel local-world-like evolving bipartite network model[J]. Acta Physica Sinica, 2012: 61(22): 558-564. [9] Li X, Chen G R. A loval-world evolving network model[J]. Phys A, 2003, 328: 274-286. [10] 胡枫, 赵海兴, 马秀娟. 一种超网络演化模型构建及特性分析[J], 中国科学: 物理学,力学,天文学, 2013, 43(1): 16-22. Hu Feng, Zhao Haixing, Ma Xiujuan. An evolving hypernetwork model and its properties[J]. Scientia Sinica Physica, Mechanica & Astronomica, 2013, 43(1): 16-22. [11] 王众托, 王志平. 超网络初探[J]. 管理学报, 2008, 5(1): 1-8. Wang Zhongtuo, Wang Zhiping. Elemen tary study of supernetworks[J]. Chinese Journal of Management, 2008, 5(1): 1-8. [12] Berge C. Graphs and Hypergraph[M]. New York: Elsevier, 2008. [13] Sheff I Y. Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods[M]. New York: Printice-Hall, 1985. [14] Nagurney A, Dong J. Supernetworks: Decision Making for the Information Age[M]. Cheltenham: Edward Elgar Publishing, 2002. [15] 董琼, 马军. 供应链超网络均衡模型[J]. 上海理工大学学报, 2011, 33(3): 238-247. Dong Qiong, Ma Jun. Recent development on supply chain supernetwork modeling[J]. J University of Shanghai for Science and Technology, 2011, 33(3): 238-247. [16] Nagurney A, Qian G Q. Fragile Networks: Identifying Vulnerabilities and Synergies in an Uncertain World[M]. New York: John Wiley & Sons, INC, 2009. [17] Nagurney A, Qian G Q. A network efficiency measure with application to critical infrastructure networks[J]. Journal of Global Optimization, 2008, 40: 261-275. [18] Albert R, BarabásiA L. Statisticmechanics of complex networks[J]. Review of Modern Physics, 2002, 74: 47297. [19] 郭进利,祝昕昀.超网络中标度的涌现[J].物理学报,2014,63(9):090207. Guo Jinli, Zhu Xinyun. Emergence of scaling in hypernetworks[J]. Acta Phys Sin, 2014, 63(9): 090207.