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网络中节点重要性度量对于研究网络的鲁棒性具有十分重要的意义. 研究者们普遍运用度或集聚系数来度量节点的重要程度, 然而度指标只考虑节点自身邻居个数而忽略了其邻居之间的信息, 集聚系数只考虑节点邻居之间的紧密程度而忽略了其邻居的规模. 本文综合考虑节点的邻居个数, 以及其邻居之间的连接紧密程度, 提出了一种基于邻居信息与集聚系数的节点重要性评价方法. 对美国航空网络和美国西部电力网进行的选择性攻击实验表明, 采用该方法的效果较k-shell指标可以分别提高24%和112%. 本文的节点重要性度量方法只需要考虑网络局部信息, 因此非常适合于对大规模网络的节点重要性进行有效分析.The node importance measurement plays an important role in analyzing the robustness of the network. Most researchers use the degree or clustering coefficient to measure the node importance. However, the degree can only take into account the neighbor size, regardless of the clustering property of the neighbors. The clustering coefficient could only measure the closeness among the neighbors and neglect the activity of the target node. In this paper, we present a new method to measure the node importance by combining neighbor and clustering coefficient information. The robustness results measured by the network efficiency through removing the important nodes for the US Air network, the power grid of the western United States and Barabasi-Albert networks show that the new method can more accurately evaluate the node importance than the degree, neighbor information and k-shell indices.
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Keywords:
- network science /
- robustness /
- node importance /
- clustering coefficient
[1] Newman M E J 2003 SIAM Rev. 45 167
[2] Barabasi A L 2009 Science 325 412
[3] Zhou T, Bai W J, Wang B H, Liu Z J, Yan G 2005 Physics 34 31 (in Chinese) [周涛, 柏文洁, 汪秉宏, 刘之景, 严钢2005 物理 34 31]
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[5] Zhou X, Zhang F M, Zhou W P, Zhou W, Yang F 2012 Acta Phys. Sin. 61 190201 (in Chinese) [周漩, 张凤鸣, 周卫平, 邹伟, 杨帆 2012 物理学报 61 190201]
[6] Tan Y J, Wu J, Deng H Z, Zhu D Z 2006 Syst. Eng. 24 1 (in Chinese) [谭跃进, 吴俊, 邓宏钟, 朱大智 2006系统工程 24 1]
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[8] Jeong H, Mason S, Barabasi A L 2001 Nature 411 41
[9] Dunne J A, Williams R J, Martinez N D 2002 Ecol. Lett. 5 558
[10] Newman M E J, Forrest S, Balthrop A 2002 J. Phys. Rev. E 66 035101
[11] Magoni D 2003 IEEE J. Sel. Area. Commun. 21 949
[12] Samant K, Bhattacharyya S 2004 Proceedings of the 37th Annual Hawaii International Conference on System Sciences Washington, USA, January 5-8, 2004 p289
[13] Freeman L C 1977 Sociometry 40 35
[14] Holme P, Kim B J, Yoon C N, Han S K 2002 Phys. Rev. E 65 056109
[15] L L Y, Zhang Y C, Yeung C H, Zhou T 2011 PLoS One 6 e21202
[16] Bryan K, Leise T 2006 SIAM Rev. 48 569
[17] Kitsak M, Gallos L K, Havlin S, Liljeros F, Muchnik L, Stanley H E, Makse H A 2010 Nat. Phys. 6 888
[18] Barabasi A L, Albert R 1999 Science 286 509
[19] Zeng A, Zhang C J 2013 Phys. Lett. A 377 1031
[20] Chen D B, Lv L Y, Shang M S, Zhang Y C, Zhou T 2011 Physica A 391 1777
[21] Centola D 2010 Science 329 1194
[22] Watts D J, Strogatz S H 1998 Nature 393 440
[23] Ugander J, Backstrom L, Marlow C, Kleinberg J 2012 Proc. Natl. Acad. Sci. 109 5962
[24] Codd E F 1970 Commun. ACM 13 377
[25] Vragovic I, Louis E, Diaz-Guilera A 2005 Phys. Rev. E 71 036122
[26] Latora V, Marchiori M 2007 New J. Phys. 9 188
[27] Li P X, Ren Y Q, Xi Y M, 2004 Syst. Eng. 22 13 (in Chinese) [李鹏翔, 任玉晴, 席酉民 系统工程 2004 22 13]
[28] He N, Li D, Gan W Y, Zhu X 2007 Comput. Sci. 34 1 (in Chinese) [赫南, 李德, 淦文燕, 朱熙 2007计算机科学 34 1]
[29] Batagelj V, Mrvar A 1998 Connections 21 47
[30] Strogatz S H 1998 Nature 393 440
[31] Klemm K, Serrano M, Eguiluz V, Miguel M 2012 Sci. Rep. 2 292
[32] Borge-Holthoefer J, Moreno Y 2012 Phys. Rev. E 85 026116
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[1] Newman M E J 2003 SIAM Rev. 45 167
[2] Barabasi A L 2009 Science 325 412
[3] Zhou T, Bai W J, Wang B H, Liu Z J, Yan G 2005 Physics 34 31 (in Chinese) [周涛, 柏文洁, 汪秉宏, 刘之景, 严钢2005 物理 34 31]
[4] Liu J G, Wang Z T, Dang Y Z 2005 Mod. Phys. Lett. B 19 785
[5] Zhou X, Zhang F M, Zhou W P, Zhou W, Yang F 2012 Acta Phys. Sin. 61 190201 (in Chinese) [周漩, 张凤鸣, 周卫平, 邹伟, 杨帆 2012 物理学报 61 190201]
[6] Tan Y J, Wu J, Deng H Z, Zhu D Z 2006 Syst. Eng. 24 1 (in Chinese) [谭跃进, 吴俊, 邓宏钟, 朱大智 2006系统工程 24 1]
[7] Liu H K, Zhou T 2007 Acta Phys. Sin. 56 106 (in Chinese) [刘宏鲲, 周涛 2007物理学报 56 106]
[8] Jeong H, Mason S, Barabasi A L 2001 Nature 411 41
[9] Dunne J A, Williams R J, Martinez N D 2002 Ecol. Lett. 5 558
[10] Newman M E J, Forrest S, Balthrop A 2002 J. Phys. Rev. E 66 035101
[11] Magoni D 2003 IEEE J. Sel. Area. Commun. 21 949
[12] Samant K, Bhattacharyya S 2004 Proceedings of the 37th Annual Hawaii International Conference on System Sciences Washington, USA, January 5-8, 2004 p289
[13] Freeman L C 1977 Sociometry 40 35
[14] Holme P, Kim B J, Yoon C N, Han S K 2002 Phys. Rev. E 65 056109
[15] L L Y, Zhang Y C, Yeung C H, Zhou T 2011 PLoS One 6 e21202
[16] Bryan K, Leise T 2006 SIAM Rev. 48 569
[17] Kitsak M, Gallos L K, Havlin S, Liljeros F, Muchnik L, Stanley H E, Makse H A 2010 Nat. Phys. 6 888
[18] Barabasi A L, Albert R 1999 Science 286 509
[19] Zeng A, Zhang C J 2013 Phys. Lett. A 377 1031
[20] Chen D B, Lv L Y, Shang M S, Zhang Y C, Zhou T 2011 Physica A 391 1777
[21] Centola D 2010 Science 329 1194
[22] Watts D J, Strogatz S H 1998 Nature 393 440
[23] Ugander J, Backstrom L, Marlow C, Kleinberg J 2012 Proc. Natl. Acad. Sci. 109 5962
[24] Codd E F 1970 Commun. ACM 13 377
[25] Vragovic I, Louis E, Diaz-Guilera A 2005 Phys. Rev. E 71 036122
[26] Latora V, Marchiori M 2007 New J. Phys. 9 188
[27] Li P X, Ren Y Q, Xi Y M, 2004 Syst. Eng. 22 13 (in Chinese) [李鹏翔, 任玉晴, 席酉民 系统工程 2004 22 13]
[28] He N, Li D, Gan W Y, Zhu X 2007 Comput. Sci. 34 1 (in Chinese) [赫南, 李德, 淦文燕, 朱熙 2007计算机科学 34 1]
[29] Batagelj V, Mrvar A 1998 Connections 21 47
[30] Strogatz S H 1998 Nature 393 440
[31] Klemm K, Serrano M, Eguiluz V, Miguel M 2012 Sci. Rep. 2 292
[32] Borge-Holthoefer J, Moreno Y 2012 Phys. Rev. E 85 026116
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