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Structural hole nodes in complex networks play important roles in the network information diffusion. Unfortunately, most of the existing methods of ranking key nodes do not integrate structural hole nodes and other key nodes. According to the relevant research on structural hole theory as well as the key node ranking methods, network constraint coefficient, betweenness centrality, hierarchy, efficiently, network size, PageRank and clustering coefficient, 7 metrics are selected to rank the key nodes. Based on the 7 metrics, a ranking learning method based on ListNet is introduced to solve ranking key nodes by multi metrics. Comprehensive experiments are conducted based on different artificial networks and real complex networks. Experimental results with manual annotation show that the ranking method can comprehensively consider the structural hole nodes and other nodes with different important features. The ranking results on different networks are highly consistent with the manual ranking results. The spreading experiment results using signed to interference ratio propagation model show that SIR model can reach a maximum propagating ratio in a shorter propagating time initiated by TOP-K key nodes selected by our method than TOP-K key nodes selected by other methods.
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Keywords:
- structural hole /
- key node /
- learning ranking /
- complex network
[1] Shen Y 2013 Chin. Phys. B 22 058903
[2] Liang Z W, Li J P, Yang F, Athina P 2014 Chin. Phys. B 23 098902
[3] Shen Y 2011 Chin. Phys. B 20 040511
[4] L L Y, Lu J A, Zhang Z K,Yan X Y,Wu Y,Shi D H,Zhou H P,Fang J Q,Zhou T 2010 Complex System and Complex Science 7 173 (in Chinese) [吕琳媛,陆君安, 张子柯, 闫小勇, 吴晔, 史定华, 周海平, 方锦清, 周涛 2010 复杂系统与复杂性科学 7 173]
[5] Burt R S 1992 Networks and Organizations: Structure, Form, and Action 65 57
[6] Bonacich P 1972 J. Math. Sociol 2 113
[7] Freeman L C 1979 Soc. Netw. 1 215
[8] Freeman L C, Borgatti S P, White D R 1991 Soc. Netw. 13 141
[9] Katz L 1953 Psychometrika 18 39
[10] Kitsak M,Gallos L K,Havlin S,Liljeros F,Muchnik L, Stanley H E, Makse H A 2010 Nature Physics 11 22
[11] Arasu A, Cho J, Garcia-Molina H 2001 ACM Transactions on Internet Technology 1 2
[12] L L, Zhang Y C, Yeung C H 2011 PLoS One E 6 21202
[13] Kleinberg J M 1999 JACM 46 604
[14] Li P X, Ren Y Q, Xi Y M 2004 System Engineering 22 13 (in Chinese) [李鹏翔, 任玉晴, 席酉民 2004 系统工程 22 13]
[15] Chen Y, Hu A Q, Hu X 2004 Journal of China Institute on Communications 25 129 (in Chinese) [陈勇, 胡爱群, 胡啸 2004 通信学报 25 129]
[16] Tan Y J, Wu J, Deng H Z 2006 System Engineering-Theory and Practice 788 79 (in Chinese) [谭跃进, 吴俊, 邓宏钟 2006 系统工程理论与实践 788 79]
[17] Zhang Y, Liu Y H, Xu K H, Luo Z R 2011 Computer Science 38 88 (in Chinese) [张翼, 刘玉华, 许凯华, 骆珍荣 2011 计算机科学 38 88]
[18] Yu H, Liu Z, Li Y J 2013 Acta Phys. Sin. 62 020204 (in Chinese) [于会, 刘尊, 李勇军 2013 物理学报 62 020204]
[19] Hou B N, Yao Y P, Liao D S 2012 Physica A 391 4021
[20] Comin C H, Costa L D 2011 Phys. Rev. E 84 056105
[21] Ren Z M, Shao F, Liu J G 2013 Acta Phys. Sin. 62 128901 (in Chinese) [任卓明, 邵凤, 刘建国 2013 物理学报 62 128901]
[22] 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 物理学报 61 050201]
[23] Burt R S 2004 American Journal of Sociology 110 349
[24] Freeman L C 1977 Sociometry 40 35
[25] Liu T Y 2009 Foundations and Trends in Information Retrieval 3 225
[26] Joachims T 2002 Proceedings of the Eighth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. Edmonton, Canada, July 23-26, 2002 p133
[27] Cao Z, Qin T, Liu T Y, Tsai M F, Hang L 2007 Proceedings of the 24th Annual international conference on Machine learning. Corvallis, June 20-24, 2007 p129
[28] Luce R D 1959 Individual Choice Behavior:A Theoretical Analysis (New York: Wiley) pp147-177
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[1] Shen Y 2013 Chin. Phys. B 22 058903
[2] Liang Z W, Li J P, Yang F, Athina P 2014 Chin. Phys. B 23 098902
[3] Shen Y 2011 Chin. Phys. B 20 040511
[4] L L Y, Lu J A, Zhang Z K,Yan X Y,Wu Y,Shi D H,Zhou H P,Fang J Q,Zhou T 2010 Complex System and Complex Science 7 173 (in Chinese) [吕琳媛,陆君安, 张子柯, 闫小勇, 吴晔, 史定华, 周海平, 方锦清, 周涛 2010 复杂系统与复杂性科学 7 173]
[5] Burt R S 1992 Networks and Organizations: Structure, Form, and Action 65 57
[6] Bonacich P 1972 J. Math. Sociol 2 113
[7] Freeman L C 1979 Soc. Netw. 1 215
[8] Freeman L C, Borgatti S P, White D R 1991 Soc. Netw. 13 141
[9] Katz L 1953 Psychometrika 18 39
[10] Kitsak M,Gallos L K,Havlin S,Liljeros F,Muchnik L, Stanley H E, Makse H A 2010 Nature Physics 11 22
[11] Arasu A, Cho J, Garcia-Molina H 2001 ACM Transactions on Internet Technology 1 2
[12] L L, Zhang Y C, Yeung C H 2011 PLoS One E 6 21202
[13] Kleinberg J M 1999 JACM 46 604
[14] Li P X, Ren Y Q, Xi Y M 2004 System Engineering 22 13 (in Chinese) [李鹏翔, 任玉晴, 席酉民 2004 系统工程 22 13]
[15] Chen Y, Hu A Q, Hu X 2004 Journal of China Institute on Communications 25 129 (in Chinese) [陈勇, 胡爱群, 胡啸 2004 通信学报 25 129]
[16] Tan Y J, Wu J, Deng H Z 2006 System Engineering-Theory and Practice 788 79 (in Chinese) [谭跃进, 吴俊, 邓宏钟 2006 系统工程理论与实践 788 79]
[17] Zhang Y, Liu Y H, Xu K H, Luo Z R 2011 Computer Science 38 88 (in Chinese) [张翼, 刘玉华, 许凯华, 骆珍荣 2011 计算机科学 38 88]
[18] Yu H, Liu Z, Li Y J 2013 Acta Phys. Sin. 62 020204 (in Chinese) [于会, 刘尊, 李勇军 2013 物理学报 62 020204]
[19] Hou B N, Yao Y P, Liao D S 2012 Physica A 391 4021
[20] Comin C H, Costa L D 2011 Phys. Rev. E 84 056105
[21] Ren Z M, Shao F, Liu J G 2013 Acta Phys. Sin. 62 128901 (in Chinese) [任卓明, 邵凤, 刘建国 2013 物理学报 62 128901]
[22] 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 物理学报 61 050201]
[23] Burt R S 2004 American Journal of Sociology 110 349
[24] Freeman L C 1977 Sociometry 40 35
[25] Liu T Y 2009 Foundations and Trends in Information Retrieval 3 225
[26] Joachims T 2002 Proceedings of the Eighth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. Edmonton, Canada, July 23-26, 2002 p133
[27] Cao Z, Qin T, Liu T Y, Tsai M F, Hang L 2007 Proceedings of the 24th Annual international conference on Machine learning. Corvallis, June 20-24, 2007 p129
[28] Luce R D 1959 Individual Choice Behavior:A Theoretical Analysis (New York: Wiley) pp147-177
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