Node influence of the dynamic networks

Ren Zhuo-Ming

doi:10.7498/aps.69.20190830

Abstract

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.

Keywords:

Authors and contacts

Ren Zhuo-Ming

Research Center for Complexity Sciences, Alibaba Business School, Hangzhou Normal University, Hangzhou 311121, China

Corresponding author: Ren Zhuo-Ming, zhuoming.ren@hznu.edu.cn

FullText HTML : translate this paragraph

References

[1]	Clauset A, Larremore D B, Sinatra R 2017 Science 355 477 Google Scholar
[2]	Ren Z M, Zeng A, Zhang Y C 2018 Phys. Rep. 750 1 Google Scholar
[3]	Lü L, Chen D, Ren X L, Zhang Q M, Zhang Y C, Zhou T 2016 Phys. Rep. 650 1 Google Scholar
[4]	Lynch C 2008 Nature 455 28 Google 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. 424 175 Google Scholar
[7]	Wang W, Tang M, Stanley H E, Braunstein L A 2017 Rep. Prog. Phys. 80 036603 Google Scholar
[8]	Zhang Z K, Liu C, Zhan X X, Lu X, Zhang C X, Zhang Y C 2016 Phys. Rep. 651 1 Google Scholar
[9]	Zeng A, Shen Z, Zhou J, Wu J, Fan Y, Wang Y, Stanley H E 2017 Phys. Rep. 714 1 Google Scholar
[10]	Schweitzer F, Fagiolo G, Sornette D, Vega-Redondo F, Vespignani A, White D R 2009 Science 325 422 Google Scholar
[11]	高见, 周涛 2016 电子科技大学学报 45 625 Google Scholar Gao J, Zhou T 2016 J. Univ. Elec. Sci. Tech. China 45 625 Google Scholar
[12]	Hidalgo C A 2018 Nat. Phys. 14 9 Google Scholar
[13]	Borgatti S P, Mehra A, Brass D J, Labianca G 2009 Science 323 892 Google Scholar
[14]	Newman M E J 2003 SIAM Rev. 45 167 Google Scholar
[15]	Gert S 1966 Psychometrika 31 581
[16]	Goh K I, Oh E, Kahng B, Kim D 2003 Phys. Rev. E 67 017101 Google Scholar
[17]	Borgatti S P 2005 Soc. Net. 27 55 Google Scholar
[18]	Kitsak M, Gallos L K, Havlin S, Liljeros F, Muchnik L, Stanley H E 2010 Nat. Phys. 6 888 Google Scholar
[19]	任卓明, 邵凤, 刘建国, 郭强, 汪秉宏 2013 物理学报 262 128901 Google Scholar Ren Z M, Shao F, Liu J G, Guo Q, Wang B H 2013 Acta Phys. Sin. 262 128901 Google Scholar
[20]	Chen D, Lü L, Shang M S, Zhang Y C, Zhou T 2012 Physica A 391 1777 Google Scholar
[21]	Zhang J, Xu X K, Li P, Zhang K, Small M 2011 Chaos 21 016107 Google Scholar
[22]	Comin C H, da Fontoura Costa L 2011 Phys. Rev. E 84 056105 Google Scholar
[23]	Poulin R, Boily M C, Masse B R 2000 Soc. Net. 22 187 Google 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 083030 Google Scholar
[26]	Zeng A, Zhang C J 2013 Phys. Lett. A 377 1031 Google Scholar
[27]	Lü L, Zhou T, Zhang Q M, Stanley H E 2016 Nat. Commun. 7 10168 Google Scholar
[28]	Travenolo B A N, Costa L F 2008 Phys. Lett. A 373 89 Google 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 48005 Google Scholar
[31]	Bryan K, Leise T 2006 SIAM Rev. 48 569 Google Scholar
[32]	Berkhin P 2005 Internet Math. 2 73 Google Scholar
[33]	Lü L, Zhang Y C, Yeung C H, Zhou T 2011 PloS One 6 e21202 Google Scholar
[34]	Kleinberg J M 1999 JACM 46 604 Google 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 P07005 Google Scholar
[37]	任卓明, 刘建国, 邵凤, 胡兆龙, 郭强 2013 物理学报 62 108902 Google Scholar Ren Z M, Liu J G, Shao F, Hu Z L, Guo Q 2013 Acta Phys. Sin. 62 108902 Google Scholar
[38]	刘建国, 任卓明, 郭强, 汪秉宏 2013 物理学报 62 178901 Google Scholar Liu J G, Ren Z M, Guo Q, Wang B H 2013 Acta Phys. Sin. 62 178901 Google Scholar
[39]	任晓龙, 吕琳媛 2014 科学通报 59 1175 Google Scholar Ren X L, Lü L Y 2014 Chin. Sci. Bull. 59 1175 Google Scholar
[40]	Pei S, Makse H A 2013 J. Stat. Mech. 2013 P12002 Google Scholar
[41]	Holme P, Saramaki J 2012 Phys. Rep. 519 97 Google Scholar
[42]	Liao H, Mariani M S, Medo M, Zhang Y C, Zhou M Y 2017 Phys. Rep. 689 1 Google Scholar
[43]	Ercsey-Ravasz M, Toroczkai Z 2010 Phys. Rev. Lett. 105 038701 Google Scholar
[44]	Ercsey-Ravasz M, Lichtenwalter R N, Chawla N V, Toroczkai Z 2012 Phys. Rev. E 85 066103 Google Scholar
[45]	Lü L, Jin C H, Zhou T 2009 Phys. Rev. E 80 046122 Google Scholar
[46]	Mariani M S, Medo M, Zhang Y C 2015 Sci. Rep. 5 16181 Google Scholar
[47]	Mariani M S, Medo M, Zhang Y C 2016 J. Informetr. 10 1207 Google Scholar
[48]	Vaccario G, Medo M, Wider N, Mariani M S 2017 J. Informetr. 11 766 Google Scholar
[49]	Wasserman M, Zeng X H T, Amaral L A N 2015 PNAS 112 1281 Google Scholar
[50]	Wasserman M, Mukherjee S, Scott K, Zeng X H, Radicchi F, Amaral L A 2015 J. Asso. Info. Sci. Tech. 66 858 Google Scholar
[51]	Walker D, Xie H, Yan K K, Maslov S 2007 J. Stat. Mech. 2007 P06010 Google Scholar
[52]	Ren Z M, Mariani M S, Zhang Y C, Medo M 2018 Phys. Rev. E 97 052311 Google Scholar
[53]	Ren Z M 2018 Physica A 513 325 Google Scholar
[54]	Watts D J, Strogatz S H 1998 Nature 393 440 Google Scholar
[55]	Newman M E J 2003 Phys. Rev. E 67 026126 Google Scholar
[56]	Foster J G, Foster DV, Grassberger P, Paczuski M 2010 PNAS 107 10815 Google Scholar
[57]	Tian L, Bashan A, Shi D N, Liu Y Y 2017 Nat. Commun. 8 14223 Google Scholar
[58]	Arenas A, Diaz−Guilera A, Kurths J, Moreno Y, Zhou C 2008 Phys. Rep. 469 93 Google Scholar
[59]	Klemm K, Serrano M A, Eguiluz V M, San Miguel M 2012 Sci. Rep. 2 292 Google Scholar
[60]	Aral S, Walker D 2012 Science 337 337 Google Scholar
[61]	Centola D 2010 Science 329 1194 Google Scholar
[62]	Bond R M, Fariss C J, Jones J J, Kramer A D, Marlow C, Settle J E, Fowler J H 2012 Nature 489 295 Google Scholar
[63]	宋玉萍, 倪静 2016 物理学报 65 028901 Google Scholar Song Y P, Ning J 2016 Acta Phys. Sin. 65 028901 Google Scholar
[64]	Ma S J, Ren Z M, Ye C M, Guo Q, Liu J G 2014 Inter. J. Mod. Phys. C 25 1450065 Google Scholar
[65]	邵凤, 郭强, 曾诗奇, 刘建国 2014 电子科技大学学报 43 174 Google Scholar Shao F, Guo Q, Zeng S Q, Liu J G 2014 J. Univ. Elec. Sci. Tech. China 43 174 Google 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 e1600028 Google 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. 2 394 Google Scholar
[71]	Lü L, Pan L, Zhou T, Zhang Y C, Stanley H E 2015 PNAS 112 2325 Google Scholar
[72]	Tacchella A, Mazzilli D, Pietronero L 2018 Nat. Phys. 14 861 Google Scholar
[73]	Cristelli M, Tacchella A, Pietronero L 2015 PloS One 10 e0117174 Google Scholar
[74]	Tacchella A, Cristelli M, Caldarelli G, Gabrielli A, Pietronero L 2012 Sci. Rep. 2 723 Google Scholar
[75]	Jara-Figueroa C, Jun B, Glaeser E L, Hidalgo C A 2018 PNAS 115 12646 Google Scholar
[76]	Hidalgo C A, Hausmann R 2009 PNAS 106 10570 Google Scholar
[77]	Hidalgo C A, Klinger B, Barabasi A L, Hausmann R 2007 Science 317 482 Google Scholar
[78]	Mariani M S, Vidmer A, Medo M, Zhang Y C 2015 Eur. Phys. J. B 88 293 Google Scholar
[79]	Wu R J, Shi G Y, Zhang Y C, Mariani M S 2016 Physica A 460 254 Google Scholar
[80]	Gao J, Zhou T 2018 Physica A 492 1591 Google Scholar
[81]	Gao J, Zhang Y C, Zhou T 2019 Phys. Rep. 817 1 Google Scholar
[82]	Almeida−Neto M, Guimaraes P, Guimaraes Jr P R, Loyola R D, Ulrich W 2008 Oikos 117 1227 Google Scholar
[83]	Mariani M S, Ren Z M, Bascompte J, Tessone C J 2019 Phys. Rep. 813 1 Google Scholar
[84]	Bustos S, Gomez C, Hausmann R, Hidalgo C A 2012 PloS One 7 e49393 Google Scholar
[85]	Liu J G, Lin J H, Guo Q, Zhou T 2016 Sci. Rep. 6 21380 Google Scholar
[86]	Barzel B, Barabasi A L 2013 Nat. Phys. 9 673 Google Scholar
[87]	Barzel B, Barabasi A L 2016 Nature 530 307 Google Scholar
[88]	Medo M 2014 Phys. Rev. E 89 032801 Google Scholar
[89]	Medo M, Cimini G, Gualdi S 2011 Phys. Rev. Lett. 107 238701 Google Scholar
[90]	Ren Z M, Shi Y Q, Liao H 2016 Physica A 453 236 Google Scholar

Cited By

图 1 动态网络示意图

Figure 1. An example of the dynamic network

DownLoad: Full-Size Img PowerPoint

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

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

DownLoad: Full-Size Img PowerPoint

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

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

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

[1]	Clauset A, Larremore D B, Sinatra R 2017 Science 355 477 Google Scholar
[2]	Ren Z M, Zeng A, Zhang Y C 2018 Phys. Rep. 750 1 Google Scholar
[3]	Lü L, Chen D, Ren X L, Zhang Q M, Zhang Y C, Zhou T 2016 Phys. Rep. 650 1 Google Scholar
[4]	Lynch C 2008 Nature 455 28 Google 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. 424 175 Google Scholar
[7]	Wang W, Tang M, Stanley H E, Braunstein L A 2017 Rep. Prog. Phys. 80 036603 Google Scholar
[8]	Zhang Z K, Liu C, Zhan X X, Lu X, Zhang C X, Zhang Y C 2016 Phys. Rep. 651 1 Google Scholar
[9]	Zeng A, Shen Z, Zhou J, Wu J, Fan Y, Wang Y, Stanley H E 2017 Phys. Rep. 714 1 Google Scholar
[10]	Schweitzer F, Fagiolo G, Sornette D, Vega-Redondo F, Vespignani A, White D R 2009 Science 325 422 Google Scholar
[11]	高见, 周涛 2016 电子科技大学学报 45 625 Google Scholar Gao J, Zhou T 2016 J. Univ. Elec. Sci. Tech. China 45 625 Google Scholar
[12]	Hidalgo C A 2018 Nat. Phys. 14 9 Google Scholar
[13]	Borgatti S P, Mehra A, Brass D J, Labianca G 2009 Science 323 892 Google Scholar
[14]	Newman M E J 2003 SIAM Rev. 45 167 Google Scholar
[15]	Gert S 1966 Psychometrika 31 581
[16]	Goh K I, Oh E, Kahng B, Kim D 2003 Phys. Rev. E 67 017101 Google Scholar
[17]	Borgatti S P 2005 Soc. Net. 27 55 Google Scholar
[18]	Kitsak M, Gallos L K, Havlin S, Liljeros F, Muchnik L, Stanley H E 2010 Nat. Phys. 6 888 Google Scholar
[19]	任卓明, 邵凤, 刘建国, 郭强, 汪秉宏 2013 物理学报 262 128901 Google Scholar Ren Z M, Shao F, Liu J G, Guo Q, Wang B H 2013 Acta Phys. Sin. 262 128901 Google Scholar
[20]	Chen D, Lü L, Shang M S, Zhang Y C, Zhou T 2012 Physica A 391 1777 Google Scholar
[21]	Zhang J, Xu X K, Li P, Zhang K, Small M 2011 Chaos 21 016107 Google Scholar
[22]	Comin C H, da Fontoura Costa L 2011 Phys. Rev. E 84 056105 Google Scholar
[23]	Poulin R, Boily M C, Masse B R 2000 Soc. Net. 22 187 Google 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 083030 Google Scholar
[26]	Zeng A, Zhang C J 2013 Phys. Lett. A 377 1031 Google Scholar
[27]	Lü L, Zhou T, Zhang Q M, Stanley H E 2016 Nat. Commun. 7 10168 Google Scholar
[28]	Travenolo B A N, Costa L F 2008 Phys. Lett. A 373 89 Google 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 48005 Google Scholar
[31]	Bryan K, Leise T 2006 SIAM Rev. 48 569 Google Scholar
[32]	Berkhin P 2005 Internet Math. 2 73 Google Scholar
[33]	Lü L, Zhang Y C, Yeung C H, Zhou T 2011 PloS One 6 e21202 Google Scholar
[34]	Kleinberg J M 1999 JACM 46 604 Google 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 P07005 Google Scholar
[37]	任卓明, 刘建国, 邵凤, 胡兆龙, 郭强 2013 物理学报 62 108902 Google Scholar Ren Z M, Liu J G, Shao F, Hu Z L, Guo Q 2013 Acta Phys. Sin. 62 108902 Google Scholar
[38]	刘建国, 任卓明, 郭强, 汪秉宏 2013 物理学报 62 178901 Google Scholar Liu J G, Ren Z M, Guo Q, Wang B H 2013 Acta Phys. Sin. 62 178901 Google Scholar
[39]	任晓龙, 吕琳媛 2014 科学通报 59 1175 Google Scholar Ren X L, Lü L Y 2014 Chin. Sci. Bull. 59 1175 Google Scholar
[40]	Pei S, Makse H A 2013 J. Stat. Mech. 2013 P12002 Google Scholar
[41]	Holme P, Saramaki J 2012 Phys. Rep. 519 97 Google Scholar
[42]	Liao H, Mariani M S, Medo M, Zhang Y C, Zhou M Y 2017 Phys. Rep. 689 1 Google Scholar
[43]	Ercsey-Ravasz M, Toroczkai Z 2010 Phys. Rev. Lett. 105 038701 Google Scholar
[44]	Ercsey-Ravasz M, Lichtenwalter R N, Chawla N V, Toroczkai Z 2012 Phys. Rev. E 85 066103 Google Scholar
[45]	Lü L, Jin C H, Zhou T 2009 Phys. Rev. E 80 046122 Google Scholar
[46]	Mariani M S, Medo M, Zhang Y C 2015 Sci. Rep. 5 16181 Google Scholar
[47]	Mariani M S, Medo M, Zhang Y C 2016 J. Informetr. 10 1207 Google Scholar
[48]	Vaccario G, Medo M, Wider N, Mariani M S 2017 J. Informetr. 11 766 Google Scholar
[49]	Wasserman M, Zeng X H T, Amaral L A N 2015 PNAS 112 1281 Google Scholar
[50]	Wasserman M, Mukherjee S, Scott K, Zeng X H, Radicchi F, Amaral L A 2015 J. Asso. Info. Sci. Tech. 66 858 Google Scholar
[51]	Walker D, Xie H, Yan K K, Maslov S 2007 J. Stat. Mech. 2007 P06010 Google Scholar
[52]	Ren Z M, Mariani M S, Zhang Y C, Medo M 2018 Phys. Rev. E 97 052311 Google Scholar
[53]	Ren Z M 2018 Physica A 513 325 Google Scholar
[54]	Watts D J, Strogatz S H 1998 Nature 393 440 Google Scholar
[55]	Newman M E J 2003 Phys. Rev. E 67 026126 Google Scholar
[56]	Foster J G, Foster DV, Grassberger P, Paczuski M 2010 PNAS 107 10815 Google Scholar
[57]	Tian L, Bashan A, Shi D N, Liu Y Y 2017 Nat. Commun. 8 14223 Google Scholar
[58]	Arenas A, Diaz−Guilera A, Kurths J, Moreno Y, Zhou C 2008 Phys. Rep. 469 93 Google Scholar
[59]	Klemm K, Serrano M A, Eguiluz V M, San Miguel M 2012 Sci. Rep. 2 292 Google Scholar
[60]	Aral S, Walker D 2012 Science 337 337 Google Scholar
[61]	Centola D 2010 Science 329 1194 Google Scholar
[62]	Bond R M, Fariss C J, Jones J J, Kramer A D, Marlow C, Settle J E, Fowler J H 2012 Nature 489 295 Google Scholar
[63]	宋玉萍, 倪静 2016 物理学报 65 028901 Google Scholar Song Y P, Ning J 2016 Acta Phys. Sin. 65 028901 Google Scholar
[64]	Ma S J, Ren Z M, Ye C M, Guo Q, Liu J G 2014 Inter. J. Mod. Phys. C 25 1450065 Google Scholar
[65]	邵凤, 郭强, 曾诗奇, 刘建国 2014 电子科技大学学报 43 174 Google Scholar Shao F, Guo Q, Zeng S Q, Liu J G 2014 J. Univ. Elec. Sci. Tech. China 43 174 Google 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 e1600028 Google 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. 2 394 Google Scholar
[71]	Lü L, Pan L, Zhou T, Zhang Y C, Stanley H E 2015 PNAS 112 2325 Google Scholar
[72]	Tacchella A, Mazzilli D, Pietronero L 2018 Nat. Phys. 14 861 Google Scholar
[73]	Cristelli M, Tacchella A, Pietronero L 2015 PloS One 10 e0117174 Google Scholar
[74]	Tacchella A, Cristelli M, Caldarelli G, Gabrielli A, Pietronero L 2012 Sci. Rep. 2 723 Google Scholar
[75]	Jara-Figueroa C, Jun B, Glaeser E L, Hidalgo C A 2018 PNAS 115 12646 Google Scholar
[76]	Hidalgo C A, Hausmann R 2009 PNAS 106 10570 Google Scholar
[77]	Hidalgo C A, Klinger B, Barabasi A L, Hausmann R 2007 Science 317 482 Google Scholar
[78]	Mariani M S, Vidmer A, Medo M, Zhang Y C 2015 Eur. Phys. J. B 88 293 Google Scholar
[79]	Wu R J, Shi G Y, Zhang Y C, Mariani M S 2016 Physica A 460 254 Google Scholar
[80]	Gao J, Zhou T 2018 Physica A 492 1591 Google Scholar
[81]	Gao J, Zhang Y C, Zhou T 2019 Phys. Rep. 817 1 Google Scholar
[82]	Almeida−Neto M, Guimaraes P, Guimaraes Jr P R, Loyola R D, Ulrich W 2008 Oikos 117 1227 Google Scholar
[83]	Mariani M S, Ren Z M, Bascompte J, Tessone C J 2019 Phys. Rep. 813 1 Google Scholar
[84]	Bustos S, Gomez C, Hausmann R, Hidalgo C A 2012 PloS One 7 e49393 Google Scholar
[85]	Liu J G, Lin J H, Guo Q, Zhou T 2016 Sci. Rep. 6 21380 Google Scholar
[86]	Barzel B, Barabasi A L 2013 Nat. Phys. 9 673 Google Scholar
[87]	Barzel B, Barabasi A L 2016 Nature 530 307 Google Scholar
[88]	Medo M 2014 Phys. Rev. E 89 032801 Google Scholar
[89]	Medo M, Cimini G, Gualdi S 2011 Phys. Rev. Lett. 107 238701 Google Scholar
[90]	Ren Z M, Shi Y Q, Liao H 2016 Physica A 453 236 Google Scholar

[1]	Li Jiang, Liu Ying, Wang Wei, Zhou Tao. Identifying influential nodes in spreading process in higher-order networks. Acta Physica Sinica, 2024, 73(4): 048901. doi: 10.7498/aps.73.20231416
[2]	Han Zhong-Ming, Li Sheng-Nan, Zheng Chen-Ye, Duan Da-Gao, Yang Wei-Jie. Link prediction model based on dynamic network representation. Acta Physica Sinica, 2020, 69(16): 168901. doi: 10.7498/aps.69.20191162
[3]	Kang Ling, Xiang Bing-Bing, Zhai Su-Lan, Bao Zhong-Kui, Zhang Hai-Feng. Identifying multiple influential nodes based on region density curve in complex networks. Acta Physica Sinica, 2018, 67(19): 198901. doi: 10.7498/aps.67.20181000
[4]	Wang Yu, Guo Jin-Li. Evaluation method of node importance in directed-weighted complex network based on multiple influence matrix. Acta Physica Sinica, 2017, 66(5): 050201. doi: 10.7498/aps.66.050201
[5]	Ruan Yi-Run, Lao Song-Yang, Wang Jun-De, Bai Liang, Hou Lü-Lin. An improved evaluating method of node spreading influence in complex network based on information spreading probability. Acta Physica Sinica, 2017, 66(20): 208901. doi: 10.7498/aps.66.208901
[6]	Han Zhong-Ming, Chen Yan, Li Meng-Qi, Liu Wen, Yang Wei-Jie. An efficient node influence metric based on triangle in complex networks. Acta Physica Sinica, 2016, 65(16): 168901. doi: 10.7498/aps.65.168901
[7]	Hu Qing-Cheng, Zhang Yong, Xu Xin-Hui, Xing Chun-Xiao, Chen Chi, Chen Xin-Hua. A new approach for influence maximization in complex networks. Acta Physica Sinica, 2015, 64(19): 190101. doi: 10.7498/aps.64.190101
[8]	Min Lei, Liu Zhi, Tang Xiang-Yang, Chen Mao, Liu San-Ya. Evaluating influential spreaders in complex networks by extension of degree. Acta Physica Sinica, 2015, 64(8): 088901. doi: 10.7498/aps.64.088901
[9]	Shu Pan-Pan, Wang Wei, Tang Ming, Shang Ming-Sheng. Discriminability of node influence in flower fractal scale-free networks. Acta Physica Sinica, 2015, 64(20): 208901. doi: 10.7498/aps.64.208901
[10]	Su Xiao-Ping, Song Yu-Rong. Leveraging neighborhood “structural holes” to identifying key spreaders in social networks. Acta Physica Sinica, 2015, 64(2): 020101. doi: 10.7498/aps.64.020101
[11]	Zhao Jia, Yu Li, Li Jing-Ru. Node influence calculation mechanism based on Bayesian and semiring algebraic model in social networks. Acta Physica Sinica, 2013, 62(13): 130201. doi: 10.7498/aps.62.130201
[12]	Hu Qing-Cheng, Yin Yan-Shen, Ma Peng-Fei, Gao Yang, Zhang Yong, Xing Chun-Xiao. A new approach to identify influential spreaders in complex networks. Acta Physica Sinica, 2013, 62(14): 140101. doi: 10.7498/aps.62.140101
[13]	Yuan Wei-Guo, Liu Yun, Cheng Jun-Jun, Xiong Fei. Empirical analysis of microblog centrality and spread influence based on Bi-directional connection. Acta Physica Sinica, 2013, 62(3): 038901. doi: 10.7498/aps.62.038901
[14]	Zhao Yan-Yan, Jiang Guo-Ping. Fault diagnosis for a class of output-coupling complex dynamical networks with time delay. Acta Physica Sinica, 2011, 60(11): 110206. doi: 10.7498/aps.60.110206
[15]	Lu Jing, Zhang Rong, Xu Zhen-Yuan. Phase synchronization between two adjacent nodes in amplitude coupled dynamical networks. Acta Physica Sinica, 2010, 59(9): 5949-5953. doi: 10.7498/aps.59.5949
[16]	Yan Xiao-Yong, Wang Ming-Sheng. Influence of growth speed on the actors’ degree distribution of collaboration networks. Acta Physica Sinica, 2010, 59(2): 851-858. doi: 10.7498/aps.59.851
[17]	Xiong Fei, Liu Yun, Si Xia-Meng, Ding Fei. Network model with synchronously increasing nodes and edges based on Web 2.0. Acta Physica Sinica, 2010, 59(10): 6889-6895. doi: 10.7498/aps.59.6889
[18]	Luo Qun, Gao Ya, Qi Ya-Nan, Wu Tong, Xu Huan, Li Li-Xiang, Yang Yi-Xian. Model reference adaptive synchronization in integration complex dynamical networks. Acta Physica Sinica, 2009, 58(10): 6809-6817. doi: 10.7498/aps.58.6809
[19]	Gao Yang, Li Li-Xiang, Peng Hai-Peng, Yang Yi-Xian, Zhang Xiao-Hong. Adaptive synchronization in united complex dynamical network with multi-links. Acta Physica Sinica, 2008, 57(4): 2081-2091. doi: 10.7498/aps.57.2081
[20]	Li Ji, Wang Bing-Hong, Jiang Pin-Qun, Zhou Tao, Wang Wen-Xu. Growing complex network model with acceleratingly increasing number of nodes. Acta Physica Sinica, 2006, 55(8): 4051-4057. doi: 10.7498/aps.55.4051

Catalog

Vol. 69, Issue 4 - 2020-02-20

Metrics

Abstract views: 13354
PDF Downloads: 414
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板