文章检索

多重网络的结构与鲁棒性

  • 李明 ,
  • 汪秉宏
展开
  • 中国科学技术大学近代物理系,合肥 230026
李明(1986-),男,安徽淮南人,博士,主要研究方向为统计物理与复杂网络。

收稿日期: 2014-09-25

  修回日期: 2015-01-07

  网络出版日期: 2026-06-22

基金资助

国家自然科学基金(11275186, 91024026);飞行器海基测量与控制联合实验室开放基金(FOM2014OF001)

The Structure and Robustness of Multilayer Networks

  • LI Ming ,
  • WANG Binghong
Expand
  • Department of Modern Physics, University of Science and Technology of China,Hefei 230026, China

Received date: 2014-09-25

  Revised date: 2015-01-07

  Online published: 2026-06-22

摘要

网络常被用来刻画个体间的组合与作用方式。但是,真实系统中的组合与相互作用方式往往并不单一,而是多种混杂。为了更为准确地描述这种实际情况,多重网络的概念被提了出来。一般来说,多重网络中会有多种连边,不同种类的连边属于系统的不同层次,用以描述系统中元素在不同层次的相互作用。这个概念的引入丰富了复杂网络与复杂系统的研究。介绍多重网络的基本概念,并对其鲁棒性进行一个简明的计算与讨论。

本文引用格式

李明 , 汪秉宏 . 多重网络的结构与鲁棒性[J]. 复杂系统与复杂性科学, 2015 , 12(2) : 32 -37 . DOI: 10.13306/j.1672-3813.2015.02.005

Abstract

Networks are usually used to describe the structural relationships of the componentsof a system. However, for a real system, individuals could interact through many different channels. So, the conception of multilayer networks has been proposed. Generally speaking,multilayer networks explicitly incorporate multiple channels of connectivity, and each channel is represented by a layer and the same nodes may have different kinds of interactions. In this paper, we will give a brief introduction to the structure and robustness of the multilayer networks.

参考文献

[1] Dorogovtsev S N, Mendes J F F. Evolution of Networks: From Biological Nets to the Internet and WWW[M]. Oxford: Clarendon Press, 2002.
[2] Newman M E J. Networks: An introduction[M]. New York: Oxford University Press, 2010.
[3] Albert R, Barabási A L. Statistical mechanics of complex networks[J]. Rev Mod Phys, 2002, 74:47.
[4] Dorogovtsev S N, Mendes J F F. Evolution of networks[J]. Adv Phys, 2002, 51:1079.
[5] Newman M E J. The structure and function of complex networks[J]. SIAM Re, 2003, 45:167.
[6] Boccaletti S, Latora V, Moreno Y, et al. Complex networks: structure and dynamics[J]. Phys Rep, 2006, 424:175.
[7] Buldyrev S V, Parshani R, Paul G, et al. Catastrophic cascade of failures in interdependent networks[J]. Nature, 2010, 464:1025.
[8] Parshani R, Buldyrev S V, Havlin S. Interdependent networks: Reducing the coupling strength leads to a change from a first to second order percolation transition[J]. Phys Rev Lett, 2010, 105:048701.
[9] Parshani R, Buldyrev S V, Havlin S. Critical effect of dependency groups on the function of networks[J]. Proc Natl Acad Sci USA, 2011, 108:1007.
[10] KurantM, Thiran P. Layered complex networks[J].Phys Rev Lett,2006,96: 138701.
[11] Granell C, Gómez S, Arenas A. Dynamical interplay between awareness and epidemic spreading in multiplex networks[J].Phys Rev Lett, 2013, 111: 128701.
[12] Nicosia V, Bianconi G, Latora V,et al.Growingmultiplex networks[J]. Phys Rev Lett, 2013, 111: 058701.
[13] Battiston F, Nicosia V, Latora V. Structural measures for multiplex networks[J].Phys Rev E, 2014, 89: 032804.
[14] Baxter G J, Dorogovtsev S N, Goltsev A V, et al. Avalanche collapse of interdependent networks[J].Phys Rev Lett,2012, 109: 248701.
[15] De Domenico M, Solé-Ribalta A, Cozzo E, et al. Mathematical formulation of multilayer networks[J].Phys Rev X, 2013, 3: 041022.
[16] D′Agostino G, Scala A. Networks of Networks: the Last Frontier of Complexity[M]. Springer,2014.
[17] Boccalettia S,Bianconic G,Criadod R, et al. The structure and dynamics of multilayer networks[DB/OL].[2014-08-12].http://arxiv.org/abs/1407.0742.
[18] Parshani R, Rozenblat C, Ietri D, et al. Inter-similarity between coupled networks[J]. Euro phys Lett, 2010, 92:68002.
[19] Lee K-M, Kim J Y, Cho W-K, et al. Correlated multiplexity and connectivity of multiplex random networks[J]. New J Phys, 2012, 14: 033027.
[20] Min B, Yi S D, Lee K-M, et al. Network robustness of multiplex networks with interlayer degree correlations[J].Phys Rev E, 2014, 89: 042811.
[21] Hu Y, Zhou D, Zhang R, et al. Percolation of interdependent networks with intersimilarity[J].Phys Rev E, 2013, 88: 052805.
[22] Cellai D, Lopez E, Zhou J, et al. Percolation in multiplex networks with overlap[J].Phys Rev E, 2013, 88: 052811.
[23] Cohen R, Erez K, Avraham D, et al. Resilience of the Internet to random breakdowns[J]. PhysRev Lett, 2000, 85:4626.
[24] Callaway D S, Newman M E J, Strogatz S H, et al. Network robustness and fragility: Percolation on random graphs[J]. Phys Rev Lett, 2000, 85:5468.
[25] Cohen R, Erez K, Avraham D, et al. Breakdown of the Internet under intentional attack[J]. Phys Rev Lett, 2001, 86:3682.
[26] Cohen R, Havlin S. Complex networks: Structure, robustness and function[M]. Cambridge:Cambridge University Press, 2010.
[27] 李明. 网络逾渗与级联故障[D]. 合肥:中国科学技术大学, 2014.
Li Ming. Percolation and cascading failures on networks[D]. Hefei: University of Science and Technology of China, 2014.
[28] Gao J, Buldyrev S V, Havlin S, et al.Robustness of a network of networks[J].Phys Rev Lett, 2011, 107: 195701.
[29] Gao J, Buldyrev S V, Stanley H E, et al.Percolation of a general network of networks[J].Phys Rev E, 2013, 88: 062816.
[30] Son S W, Bizhani G, Christensen C, et al. Percolation theory on interdependent networks based on epidemic spreading[J]. Euro Phys Lett, 2012, 97:16006.
[31] Newman M E J, Strogatz S H, Watts D J. Random graphs with arbitrary degree distributionsand their applications[J]. Phys Rev E, 2001, 64:026118.
[32] Newman M E J. Spread of epidemic disease on networks[J]. Phys Rev E, 2002, 66:016128.
[33] Brummitt C D, Lee K-M, Goh K-I.Multiplexity-facilitated cascades in networks[J].Phys Rev E, 2012, 85: 045102.
[34] Brummitt C D, D′Souza R M, Leicht E A, Suppressing cascades of load in interdependent networks[J].Proc Natl Acad Sci USA, 2012, 109: E680.
[35] Kurant M, Thiran P,HagmannP. Error and attack tolerance of layered complex networks[J].Phys Rev E, 2007, 76: 026103.
[36] Gómez S, Díaz-Guilera A, Gómez-Gardees J, et al. Diffusion dynamics on multiplex networks[J].Phys Rev Lett, 2013,110: 028701.
[37] Buldyrev S V, Shere N W, CwilichG A. Interdependent networks with identical degrees of mutually dependent nodes[J].Phys Rev E, 2011, 83: 016112.
[38] Valdez L D, Macri P A, Stanley H E, et al. Triple point in correlated interdependent networks[J].Phys Rev E, 2013, 88: 050803.
[39] Li M, Liu R-R, Jia C-X, et al. Critical effects of overlapping of connectivity and dependence links on percolation of networks[J]. New J Phys, 2013, 15: 093013.
[40] Newman M E J. Mixing patterns in networks[J]. Phys Rev E, 2003, 67:026126.
[41] Vázquez A, Moreno Y. Resilience to damage of graphs with degree correlations[J]. Phys Rev E, 2003, 67:015101.
[42] Zhou D, Stanley H E,D′Agostino G, et al.Assortativity decreases the robustness of interdependent networks[J].Phys Rev E, 2012, 86: 066103.
[43] Kim J-Y, Goh K-I. Coevolution and correlated multiplexity in multiplex networks[J].Phys Rev Lett,2013, 111: 058702.
文章导航

/

〈 〉