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动态复杂网络中节点影响力的研究进展

任卓明

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动态复杂网络中节点影响力的研究进展

任卓明

Node influence of the dynamic networks

Ren Zhuo-Ming
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  • 节点影响力的识别和预测具有重要的理论意义和应用价值, 是复杂网络的热点研究领域. 目前大多数研究方法都是针对静态网络或动态网络某一时刻的快照进行的, 然而在实际应用场景中, 社会、生物、信息、技术等复杂网络都是动态演化的. 因此在动态复杂网络中评估节点影响力以及预测节点未来影响力, 特别是在网络结构变化之前的预测更具意义. 本文系统地总结了动态复杂网络中节点影响力算法面临的三类挑战, 即在增长网络中, 节点影响力算法的计算复杂性和时间偏见; 网络实时动态演化时, 节点影响力算法的适应性; 网络结构微扰或突变时, 节点影响力算法的鲁棒性, 以及利用网络结构演变阐释经济复杂性涌现的问题. 最后总结了这一研究方向几个待解决的问题并指出未来可能的发展方向.
    Crucial to the physicists’ strong interest in the field is the fact that such macroscopic properties typically arise as the result of a myriad of interactions between the system constituents. Network science aims at simplifying the study of a given complex system by representing it as a network, a collection of nodes and edges interconnecting them. Nowadays, it is widely recognized that some of the structural traits of networks are in fact ubiquitous properties in real systems. The identification and prediction of node influence are of great theoretical and practical significance to be known as a hot research field of complex networks. Most of current research advance is focused on static network or a snapshot of dynamic networks at a certain moment. However, in practical application scenarios, mostly complex networks extracted from society, biology, information, technology are evolving dynamically. Therefore, it is more meaningful to evaluate the node's influence in the dynamic network and predict the future influence of the node, especially before the change of the network structure. In this summary, we contribute on reviewing the improvement of node influence in dynamical networks, which involves three tasks: algorithmic complexity and time bias in growing networks; algorithmic applicability in time varying networks; algorithmic robustness in a dynamical network with small or sharp perturbation. Furthermore, we overview the framework of economic complexity based on dynamical network structure. Lastly, we point out the forefront as well as critical challenges of the field.
      通信作者: 任卓明, zhuoming.ren@hznu.edu.cn
    • 基金项目: 国家级-基于雪崩电离的磁阻效应及其机理研究(61673151,61873080,61803137)
      Corresponding author: Ren Zhuo-Ming, zhuoming.ren@hznu.edu.cn
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  • 图 1  动态网络示意图

    Fig. 1.  An example of the dynamic network

    图 2  局部到全局的渐进式算法的示意图 (a) 全局算法; (b) 渐进式算法

    Fig. 2.  The diagram of local to global progressive algorithm: (a) Global algorithm; (b) The local to global progressive algorithm.

    图 3  实时动态网络 (a) 含有一段时间的网络; (b) 动态演化网络

    Fig. 3.  An example of the time-variant dynamic network: (a) A network with a period of time; (b) the time-variant dynamic network.

    图 4  4种经典节点影响力算法(度、紧密度、介数、特征向量中心性)在可变度-度相关性的无标度网络中准确性, 其中β表示传播参数, r表示可变度-度相关性的无标度网络中的度- 度相关性参数, Kendall's tau值大小表示节点影响力方法的准确性

    Fig. 4.  The accuracy analysis of four centrality (degree, closeness, betweenness, eigenvector) methods on the scale-free network model with tunable assortative coefficient r and different infectious rate β.

    图 5  邻接矩阵的嵌套性示意图 (a) 邻接矩阵的嵌套值为0; (b) 邻接矩阵的嵌套值为0.5; (c) 邻接矩阵的嵌套值为1

    Fig. 5.  The nestedness of the adjacency matrix: (a) The nestedness of the adjacency matrix is 0; (b)the nestedness of the adjacency matrix is 0.5; (c)the nestedness of the adjacency matrix is 1.

    图 6  786类商品国际贸易网络的嵌套性分布图, 其中子图为牛肉、摩托车、医疗器械三类不同商品的国际贸易网络的可视化邻接矩阵

    Fig. 6.  Distribution of the nestedness in the international trade networks with 786 kinds of goods. (subgraphs) The matrices are representations of the different layer of world trade networks which respectively corresponds to the network of Bovine, Motorcycles, and Medical Instruments.

  • [1]

    Clauset A, Larremore D B, Sinatra R 2017 Science 355 477Google Scholar

    [2]

    Ren Z M, Zeng A, Zhang Y C 2018 Phys. Rep. 750 1Google Scholar

    [3]

    Lü L, Chen D, Ren X L, Zhang Q M, Zhang Y C, Zhou T 2016 Phys. Rep. 650 1Google Scholar

    [4]

    Lynch C 2008 Nature 455 28Google Scholar

    [5]

    Mariani M S, Ren Z M, Bascompte J, Tessone C J 2019 Physics Reports 813 1

    [6]

    Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang D U 2006 Phys. Rep. 424 175Google Scholar

    [7]

    Wang W, Tang M, Stanley H E, Braunstein L A 2017 Rep. Prog. Phys. 80 036603Google Scholar

    [8]

    Zhang Z K, Liu C, Zhan X X, Lu X, Zhang C X, Zhang Y C 2016 Phys. Rep. 651 1Google Scholar

    [9]

    Zeng A, Shen Z, Zhou J, Wu J, Fan Y, Wang Y, Stanley H E 2017 Phys. Rep. 714 1Google Scholar

    [10]

    Schweitzer F, Fagiolo G, Sornette D, Vega-Redondo F, Vespignani A, White D R 2009 Science 325 422Google Scholar

    [11]

    高见, 周涛 2016 电子科技大学学报 45 625Google Scholar

    Gao J, Zhou T 2016 J. Univ. Elec. Sci. Tech. China 45 625Google Scholar

    [12]

    Hidalgo C A 2018 Nat. Phys. 14 9Google Scholar

    [13]

    Borgatti S P, Mehra A, Brass D J, Labianca G 2009 Science 323 892Google Scholar

    [14]

    Newman M E J 2003 SIAM Rev. 45 167Google Scholar

    [15]

    Gert S 1966 Psychometrika 31 581

    [16]

    Goh K I, Oh E, Kahng B, Kim D 2003 Phys. Rev. E 67 017101Google Scholar

    [17]

    Borgatti S P 2005 Soc. Net. 27 55Google Scholar

    [18]

    Kitsak M, Gallos L K, Havlin S, Liljeros F, Muchnik L, Stanley H E 2010 Nat. Phys. 6 888Google Scholar

    [19]

    任卓明, 邵凤, 刘建国, 郭强, 汪秉宏 2013 物理学报 262 128901Google Scholar

    Ren Z M, Shao F, Liu J G, Guo Q, Wang B H 2013 Acta Phys. Sin. 262 128901Google Scholar

    [20]

    Chen D, Lü L, Shang M S, Zhang Y C, Zhou T 2012 Physica A 391 1777Google Scholar

    [21]

    Zhang J, Xu X K, Li P, Zhang K, Small M 2011 Chaos 21 016107Google Scholar

    [22]

    Comin C H, da Fontoura Costa L 2011 Phys. Rev. E 84 056105Google Scholar

    [23]

    Poulin R, Boily M C, Masse B R 2000 Soc. Net. 22 187Google Scholar

    [24]

    Pei S, Morone F, Makse H A 2018 Theories for Influencer Identification in Complex Networks. In: Lehmann S, Ahn YY. (Ed.) Complex Spreading Phenomena in Social Systems. Computational Social Sciences. Springer, Cham pp125–148

    [25]

    Garas A, Schweitzer F, Havlin S 2012 New J. Phys. 14 083030Google Scholar

    [26]

    Zeng A, Zhang C J 2013 Phys. Lett. A 377 1031Google Scholar

    [27]

    Lü L, Zhou T, Zhang Q M, Stanley H E 2016 Nat. Commun. 7 10168Google Scholar

    [28]

    Travenolo B A N, Costa L F 2008 Phys. Lett. A 373 89Google Scholar

    [29]

    Chen D B, Xiao R, Zeng A, Zhang Y C 2014 EPL 104 68006

    [30]

    Ren Z M, Zeng A, Chen D B, Liao H, Liu J G 2014 EPL 106 48005Google Scholar

    [31]

    Bryan K, Leise T 2006 SIAM Rev. 48 569Google Scholar

    [32]

    Berkhin P 2005 Internet Math. 2 73Google Scholar

    [33]

    Lü L, Zhang Y C, Yeung C H, Zhou T 2011 PloS One 6 e21202Google Scholar

    [34]

    Kleinberg J M 1999 JACM 46 604Google Scholar

    [35]

    Newman M E J 2016 New Palg. Dict. Econ. 2016 1

    [36]

    Da Silva R A P, Viana M P, da Fontoura Costa L 2012 J. Stat. Mech. 2012 P07005Google Scholar

    [37]

    任卓明, 刘建国, 邵凤, 胡兆龙, 郭强 2013 物理学报 62 108902Google Scholar

    Ren Z M, Liu J G, Shao F, Hu Z L, Guo Q 2013 Acta Phys. Sin. 62 108902Google Scholar

    [38]

    刘建国, 任卓明, 郭强, 汪秉宏 2013 物理学报 62 178901Google Scholar

    Liu J G, Ren Z M, Guo Q, Wang B H 2013 Acta Phys. Sin. 62 178901Google Scholar

    [39]

    任晓龙, 吕琳媛 2014 科学通报 59 1175Google Scholar

    Ren X L, Lü L Y 2014 Chin. Sci. Bull. 59 1175Google Scholar

    [40]

    Pei S, Makse H A 2013 J. Stat. Mech. 2013 P12002Google Scholar

    [41]

    Holme P, Saramaki J 2012 Phys. Rep. 519 97Google Scholar

    [42]

    Liao H, Mariani M S, Medo M, Zhang Y C, Zhou M Y 2017 Phys. Rep. 689 1Google Scholar

    [43]

    Ercsey-Ravasz M, Toroczkai Z 2010 Phys. Rev. Lett. 105 038701Google Scholar

    [44]

    Ercsey-Ravasz M, Lichtenwalter R N, Chawla N V, Toroczkai Z 2012 Phys. Rev. E 85 066103Google Scholar

    [45]

    Lü L, Jin C H, Zhou T 2009 Phys. Rev. E 80 046122Google Scholar

    [46]

    Mariani M S, Medo M, Zhang Y C 2015 Sci. Rep. 5 16181Google Scholar

    [47]

    Mariani M S, Medo M, Zhang Y C 2016 J. Informetr. 10 1207Google Scholar

    [48]

    Vaccario G, Medo M, Wider N, Mariani M S 2017 J. Informetr. 11 766Google Scholar

    [49]

    Wasserman M, Zeng X H T, Amaral L A N 2015 PNAS 112 1281Google Scholar

    [50]

    Wasserman M, Mukherjee S, Scott K, Zeng X H, Radicchi F, Amaral L A 2015 J. Asso. Info. Sci. Tech. 66 858Google Scholar

    [51]

    Walker D, Xie H, Yan K K, Maslov S 2007 J. Stat. Mech. 2007 P06010Google Scholar

    [52]

    Ren Z M, Mariani M S, Zhang Y C, Medo M 2018 Phys. Rev. E 97 052311Google Scholar

    [53]

    Ren Z M 2018 Physica A 513 325Google Scholar

    [54]

    Watts D J, Strogatz S H 1998 Nature 393 440Google Scholar

    [55]

    Newman M E J 2003 Phys. Rev. E 67 026126Google Scholar

    [56]

    Foster J G, Foster DV, Grassberger P, Paczuski M 2010 PNAS 107 10815Google Scholar

    [57]

    Tian L, Bashan A, Shi D N, Liu Y Y 2017 Nat. Commun. 8 14223Google Scholar

    [58]

    Arenas A, Diaz−Guilera A, Kurths J, Moreno Y, Zhou C 2008 Phys. Rep. 469 93Google Scholar

    [59]

    Klemm K, Serrano M A, Eguiluz V M, San Miguel M 2012 Sci. Rep. 2 292Google Scholar

    [60]

    Aral S, Walker D 2012 Science 337 337Google Scholar

    [61]

    Centola D 2010 Science 329 1194Google Scholar

    [62]

    Bond R M, Fariss C J, Jones J J, Kramer A D, Marlow C, Settle J E, Fowler J H 2012 Nature 489 295Google Scholar

    [63]

    宋玉萍, 倪静 2016 物理学报 65 028901Google Scholar

    Song Y P, Ning J 2016 Acta Phys. Sin. 65 028901Google Scholar

    [64]

    Ma S J, Ren Z M, Ye C M, Guo Q, Liu J G 2014 Inter. J. Mod. Phys. C 25 1450065Google Scholar

    [65]

    邵凤, 郭强, 曾诗奇, 刘建国 2014 电子科技大学学报 43 174Google Scholar

    Shao F, Guo Q, Zeng S Q, Liu J G 2014 J. Univ. Elec. Sci. Tech. China 43 174Google Scholar

    [66]

    Lambiotte R, Rosvall M, Scholtes I 2018 arXiv preprint arXiv 1806 05977

    [67]

    Perri V, Scholtes I 2019 arXiv preprint arXiv 1908 05976

    [68]

    Xu J, Wickramarathne T L, Chawla N V 2016 Sci. Adv. 2 e1600028Google Scholar

    [69]

    Tao J, Xu J, Wang C, Chawla N V 2017 IEEE Paci. Vis. Symp. (PacificVis) 2 1

    [70]

    Ghoshal G, Barabasi A L 2011 Nat. Commun. 2 394Google Scholar

    [71]

    Lü L, Pan L, Zhou T, Zhang Y C, Stanley H E 2015 PNAS 112 2325Google Scholar

    [72]

    Tacchella A, Mazzilli D, Pietronero L 2018 Nat. Phys. 14 861Google Scholar

    [73]

    Cristelli M, Tacchella A, Pietronero L 2015 PloS One 10 e0117174Google Scholar

    [74]

    Tacchella A, Cristelli M, Caldarelli G, Gabrielli A, Pietronero L 2012 Sci. Rep. 2 723Google Scholar

    [75]

    Jara-Figueroa C, Jun B, Glaeser E L, Hidalgo C A 2018 PNAS 115 12646Google Scholar

    [76]

    Hidalgo C A, Hausmann R 2009 PNAS 106 10570Google Scholar

    [77]

    Hidalgo C A, Klinger B, Barabasi A L, Hausmann R 2007 Science 317 482Google Scholar

    [78]

    Mariani M S, Vidmer A, Medo M, Zhang Y C 2015 Eur. Phys. J. B 88 293Google Scholar

    [79]

    Wu R J, Shi G Y, Zhang Y C, Mariani M S 2016 Physica A 460 254Google Scholar

    [80]

    Gao J, Zhou T 2018 Physica A 492 1591Google Scholar

    [81]

    Gao J, Zhang Y C, Zhou T 2019 Phys. Rep. 817 1Google Scholar

    [82]

    Almeida−Neto M, Guimaraes P, Guimaraes Jr P R, Loyola R D, Ulrich W 2008 Oikos 117 1227Google Scholar

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出版历程
  • 收稿日期:  2019-05-28
  • 修回日期:  2019-11-26
  • 刊出日期:  2020-02-20

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