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In complex networks, it is significant how to rank the nodes according to their importance. Most of the existing methods of ranking key nodes (e.g. degree-based, betweenness-based) only consider one factor but not the integration of whole complex network in evaluating the importance of nodes, so those methods each have a limited application range. In this paper, a multi-attribute decision-making method to identify the key nodes in complex networks is proposed. In our method, each node is regarded as a solution, and each importance evaluation criterion as one solution's attribute. After that, we calculate the closeness between each solution and the ideal solution in order to obtain the integration results of node importance in complex networks. The proposed method can be used in a variety of complex networks. It is also easy to evaluate the importance evaluation criteria. Finally, experimental results show that the proposed method is effective.
[1] Barabási A L, Bonabeau E 2003 Sci. Am. 288 50
[2] Chen H, Chung W, Xu J J, Wang G, Qin Y, Chau M 2004 Computer 37 50
[3] L T Y, Piao X F, Xie W Y, Huang S B 2012 Acta Phys. Sin. 61 170512 (in Chinese) [吕天阳, 朴秀峰, 谢文艳, 黄少滨 2012 61 170512]
[4] Xu D, Li X, Wang X F 2007 Acta Phys. Sin. 56 1313 (in Chinese) [许丹, 李翔, 汪小帆 2007 56 1313]
[5] Xiong X, Hu Y 2012 Acta Phys. Sin. 61 150509 (in Chinese) [熊熙, 胡勇 2012 61 150509]
[6] Budak C, Agrawal D, Abbadi A E 2011 Proceedings of the International World Wide Web Conference Committee Hyderabad, India, March 28-April 1, 2011 p665
[7] Zhang Y C, Liu Y, Zhang H F, Cheng H, Xiong F 2011 Acta Phys. Sin. 60 050501 (in Chinese) [张彦超, 刘云, 张海峰, 程辉, 熊菲 2011 60 050501]
[8] Yan R, Tang J, Liu X B 2011 Proceedings of the 20th ACM international conference on Information and knowledge management, Glasgow, Scotland, UK, October 24-28, 2011 p1247
[9] Watts D J, Dodds P S, Newman M E J 2002 Science 296 1302
[10] Liu H K, Zhou T 2007 Acta Phys. Sin. 56 106 (in Chinese) [刘宏鲲, 周涛 2007 56 106]
[11] Cai K Q, Zhang Jun, Du W B, Cao X B 2012 Chin. Phys. B 21 028903
[12] Wang G Z, Gao Y J, Bao Z J, Han Z X 2009 Acta Phys. Sin. 58 3597 (in Chinese) [王光增, 曹一家, 包哲静, 韩帧祥 2009 58 3597]
[13] Kinney R, Crucitti P, Albert R, Latora V 2005 Eur. Phys. J. B 46 101
[14] An S H, Du Y B, Qu J L 2006 Chin. J. Manage. Sci. 14 106 (in Chinese) [安世虎, 都艺兵, 曲吉林 2006 中国管理科学 14 106]
[15] Corley H W, Sha D Y 1982 Oper. Res. Letters 1 157
[16] Nardelli E, Proietti G, Widmayer P 2001 Info. Proc. Letters 79 81
[17] Tan Y J, Wu J, Deng H Z 2006 Syst. Eng. Theory & Practice 26 79 (in Chinese) [谭跃进, 吴俊, 邓宏钟 2006 系统工程理论与实践 26 79]
[18] Freeman L C, Borgatti S P, White D R 1991 Soc. Networks 13 141
[19] Luo J D 2010 Social Network Analysis (2st Ed.) (Beijing: Social Science Academic Press) p187 (in Chinese) [罗家德 2010 社会网分析讲义(北京:社会科学文献出版社) 第187页]
[20] Estrada E, Rodríguez-Velázquez J A 2005 Phy. Rev. E 71 056103
[21] Perra N, Fortunato S 2008 Phy. Rev. E 78 036107
[22] Newman M E J 2005 Soc. Networks 27 39
[23] Dou F L, Hu Y Q, Li Y, Fan Y, Di Z R Acta Phys. Sin. 61 178901 (in Chinese) [钭斐玲, 胡延庆, 黎勇, 樊瑛, 狄增如 2012 61 178901]
[24] Tzeng G H, Huang J J 2011 Multiple Attribute Decision Making: Methods and Applications (CRC: Boca Raton London New York) p69
[25] Wang X F, Li X, Chen G R 2012 Network Science: An Introduction (1st Ed.) (Beijing: Higher Education Press) p161 (in Chinese) [汪小帆, 李翔, 陈关荣 2012 网络科学导论(北京:高等教育出版社) 第161页]
[26] Freeman L C A 1977 Sociometry 40 35
[27] Burt R S 2004 Am. J. Sociol. 110 349
[28] Zhu Y, Meng Z Y, Kan S Y 1999 J. Northern Jiaotong University 23 119 (in Chinese) [朱茵, 孟志勇, 阚叔愚 1999 北方交通大学学报 23 119]
[29] Zhou X, Zhang F M, Li K W, Hui X B, Wu H S 2012 Acta Phys. Sin. 61 050201 (in Chinese) [周漩, 张凤鸣, 李克武, 惠晓滨, 吴虎胜 2012 61 050201]
[30] Chen Y, Hu A Q, Hu X 2004 J. China Institute Commun. 25 129 (in Chinese) [陈勇, 胡爱群, 胡啸 2004 通信学报 25 129]
[31] Zhao Y H,Wang Z L, Zheng J, Guo X J 2009 J. Beijing University of Aeronautics and Astronautics 35 1076 (in Chinese) [赵毅寰, 王祖林, 郑晶, 郭旭静 2009 北京航空航天大学学报 35 1076]
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[1] Barabási A L, Bonabeau E 2003 Sci. Am. 288 50
[2] Chen H, Chung W, Xu J J, Wang G, Qin Y, Chau M 2004 Computer 37 50
[3] L T Y, Piao X F, Xie W Y, Huang S B 2012 Acta Phys. Sin. 61 170512 (in Chinese) [吕天阳, 朴秀峰, 谢文艳, 黄少滨 2012 61 170512]
[4] Xu D, Li X, Wang X F 2007 Acta Phys. Sin. 56 1313 (in Chinese) [许丹, 李翔, 汪小帆 2007 56 1313]
[5] Xiong X, Hu Y 2012 Acta Phys. Sin. 61 150509 (in Chinese) [熊熙, 胡勇 2012 61 150509]
[6] Budak C, Agrawal D, Abbadi A E 2011 Proceedings of the International World Wide Web Conference Committee Hyderabad, India, March 28-April 1, 2011 p665
[7] Zhang Y C, Liu Y, Zhang H F, Cheng H, Xiong F 2011 Acta Phys. Sin. 60 050501 (in Chinese) [张彦超, 刘云, 张海峰, 程辉, 熊菲 2011 60 050501]
[8] Yan R, Tang J, Liu X B 2011 Proceedings of the 20th ACM international conference on Information and knowledge management, Glasgow, Scotland, UK, October 24-28, 2011 p1247
[9] Watts D J, Dodds P S, Newman M E J 2002 Science 296 1302
[10] Liu H K, Zhou T 2007 Acta Phys. Sin. 56 106 (in Chinese) [刘宏鲲, 周涛 2007 56 106]
[11] Cai K Q, Zhang Jun, Du W B, Cao X B 2012 Chin. Phys. B 21 028903
[12] Wang G Z, Gao Y J, Bao Z J, Han Z X 2009 Acta Phys. Sin. 58 3597 (in Chinese) [王光增, 曹一家, 包哲静, 韩帧祥 2009 58 3597]
[13] Kinney R, Crucitti P, Albert R, Latora V 2005 Eur. Phys. J. B 46 101
[14] An S H, Du Y B, Qu J L 2006 Chin. J. Manage. Sci. 14 106 (in Chinese) [安世虎, 都艺兵, 曲吉林 2006 中国管理科学 14 106]
[15] Corley H W, Sha D Y 1982 Oper. Res. Letters 1 157
[16] Nardelli E, Proietti G, Widmayer P 2001 Info. Proc. Letters 79 81
[17] Tan Y J, Wu J, Deng H Z 2006 Syst. Eng. Theory & Practice 26 79 (in Chinese) [谭跃进, 吴俊, 邓宏钟 2006 系统工程理论与实践 26 79]
[18] Freeman L C, Borgatti S P, White D R 1991 Soc. Networks 13 141
[19] Luo J D 2010 Social Network Analysis (2st Ed.) (Beijing: Social Science Academic Press) p187 (in Chinese) [罗家德 2010 社会网分析讲义(北京:社会科学文献出版社) 第187页]
[20] Estrada E, Rodríguez-Velázquez J A 2005 Phy. Rev. E 71 056103
[21] Perra N, Fortunato S 2008 Phy. Rev. E 78 036107
[22] Newman M E J 2005 Soc. Networks 27 39
[23] Dou F L, Hu Y Q, Li Y, Fan Y, Di Z R Acta Phys. Sin. 61 178901 (in Chinese) [钭斐玲, 胡延庆, 黎勇, 樊瑛, 狄增如 2012 61 178901]
[24] Tzeng G H, Huang J J 2011 Multiple Attribute Decision Making: Methods and Applications (CRC: Boca Raton London New York) p69
[25] Wang X F, Li X, Chen G R 2012 Network Science: An Introduction (1st Ed.) (Beijing: Higher Education Press) p161 (in Chinese) [汪小帆, 李翔, 陈关荣 2012 网络科学导论(北京:高等教育出版社) 第161页]
[26] Freeman L C A 1977 Sociometry 40 35
[27] Burt R S 2004 Am. J. Sociol. 110 349
[28] Zhu Y, Meng Z Y, Kan S Y 1999 J. Northern Jiaotong University 23 119 (in Chinese) [朱茵, 孟志勇, 阚叔愚 1999 北方交通大学学报 23 119]
[29] Zhou X, Zhang F M, Li K W, Hui X B, Wu H S 2012 Acta Phys. Sin. 61 050201 (in Chinese) [周漩, 张凤鸣, 李克武, 惠晓滨, 吴虎胜 2012 61 050201]
[30] Chen Y, Hu A Q, Hu X 2004 J. China Institute Commun. 25 129 (in Chinese) [陈勇, 胡爱群, 胡啸 2004 通信学报 25 129]
[31] Zhao Y H,Wang Z L, Zheng J, Guo X J 2009 J. Beijing University of Aeronautics and Astronautics 35 1076 (in Chinese) [赵毅寰, 王祖林, 郑晶, 郭旭静 2009 北京航空航天大学学报 35 1076]
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