通过建立3 种典型的复杂网络模型及对应的输运模型,数值计算并仿真试验拓扑结构指标和网络承载能力的变化.结果显示:3 种网络承载能力的数值计算结果和仿真试验结果基本吻合;核心节点的存在使得无标度网络的节点最大介数值所占比重高于其他网络,导致网络的承载能力最小;随机网络的节点最大介数值所占比重低于其他网络,导致承载能力最大;随着平均度的增大,各类型网络承载能力增加明显,但各种拓扑结构指标对承载能力提升的贡献不同.
Three typical complex network models and corresponding traffic routing models were established to carry out numerical computation and simulation of topological indicators and network capacity, and empirical analysis of how network capacity is influenced by network topology was conducted. The results show that numerical calculation results and experimental results of the capacity of three different networks were roughly consistent. With existence of the core node, scale-free network had the shortest average travel path, and the proportion of the largest betweenness was much higher than that in other networks, leading to minimum capacity of the scale-free network; the proportion of the largest betweenness of nodes in random network was lower than that in other networks, leading to maximum capacity of the random network. The increase of average degree resulted in significant increase of network capacity, but the contribution of different topological indicators was not the same. Understanding the quantitative relation between network topology and network capacity is beneficial to conducting effective prevention and intervention concerning dynamic processes in the network.
[1] Watts D J, Strogatz S H. Collective dynamics of small world networks[J]. Nature, 1998, 393(6684): 440-442.
[2] Barabási A L, Albert R. Emergence of scaling in random networks[J]. Science, 1999, 286(5439): 509-512.
[3] Albert R, Barabási A L. Statistical mechanics of complex networks[J]. Reviews of Modern Physics, 2002, 74: 47-97.
[4] Toroczkai Z, Bassler K E. Network dynamics: Jamming is limited in scale-free systems[J]. Nature, 2004, 428(6984): 716-716.
[5] Arenas A, Díaz Guilera A, Guimera R. Communication in networks with hierarchical branching[J]. Physical Review Letters, 2001, 86(14): 3196.
[6] Moreno Y, Gómez J B, Pacheco A F. Instability of scale-free networks under node- breaking avalanches[J]. Europhysics Letters, 2002, 58(4): 630-636.
[7] Motter A E, Lai Y C. Cascade-based attacks on complex networks[J]. Physical Review E, 2002, 66(6): 065102.
[8] Newman M E J, Strogatz S H, Watts D J. Random graphs with arbitrary degree distributions and their applications[J]. Physical Review E, 2001, 64(2): 026118.
[9] 田旭光, 朱元昌, 邸彦强. 复杂网络抗毁性优化问题的研究[J]. 系统科 学学报, 2014(1): 60-65. Tian Xuguang, Zhu Yuanchang, Di Yanqiang. Survey on optimization for invulnerability of complex networks[J]. Journal of Systems Science, 2014(1): 60-65.
[10] Qu Z H, Wang P, Song C M, et al. Enhancement of scale- free network attack tolerance[J]. Chinese Physics B, 2010, 19(11): 110504.
[11] Zhao L, Lai Y C, Park K, et al. Onset of traffic congestion in complex networks[J]. Physical Review E, 2005, 71(2): 026125.
[12] Tadić B, Thurner S, Rodgers G J. Traffic on complex networks: Towards understanding global statistical properties from microscopic density fluctuations[J]. Physical Review E, 2004, 69(3): 036102.
[13] Guimerà R, Diaz Guilera A, Vega Redondo F, et al. Optimal network topologies for local search with congestion[J]. Physical Review Letters, 2002, 89(24): 248701.
[14] Tadić B, Rodgers G J, Thurner S. Transport on complex networks: Flow, jamming and optimization[J]. International Journal of Bifurcation and Chaos, 2007, 17(07): 2363-2385.
