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k-核分解排序法对于度量复杂网络上重要节点的传播影响力具有重要的理论意义和应用价值，但其排序粗粒化的缺陷也不容忽视.最新研究发现，一些真实网络中存在局域连接稠密的特殊构型是导致上述问题的根本原因之一.当前的解决方法是利用边两端节点的外部连边数度量边的扩散性，采取过滤网络边来减少这种稠密结构给k-核分解过程造成的干扰，但这种方法并没有考虑现实网络上存在权重的普遍性.本文利用节点权重和权重分布重新定义边的扩散性，提出适用于加权网络结构的基于冗余边过滤的k-核分解排序算法：filter-core.通过世界贸易网、线虫脑细胞网和科学家合著网等真实网络的SIR（susceptible-infected-recovered）传播模型的仿真结果表明，该算法相比其他加权k-核分解法，能够更准确地度量加权网络上具有重要传播影响力的核心节点及核心层.The k-shell decomposition method of identifying the influential nodes which accelerate spread or hinder propagation, plays an important role in analyzing the spreading performance of complex network, but it is too coarse in terms of ranking granularity. Recent study shows that the accuracy of the k-shell decomposition method in determining node coreness is significantly affected by the mutually densely connected local structures. Existing approach tries to filter out the confusion of the classical k-shell decomposition method, caused by such densely local structures, through redefining a diffusion importance value which is the number of out-leaving links at/from the nodes connected by a link. This value is used to quantify the potential influence of a link in spreading process. However, the existing approach is not suitable for ubiquitously weighted networks. In this paper, we develop a new ranking approach (filter-core) to identify the node spreading influence in weighted network. Here, we concern that the redundant links, although they are less important in the spreading process, form mutually densely connected local structures, which lead to the classical k-shell decomposition method unable to accurately determine the coreness of node in network. By redefining a new diffusion importance value for each link based on the weights of its connected nodes and the weight distribution, we filter out the redundant links which have a relatively low diffusion importance in the spreading process. After filtering out all redundant links and applying the classical k-shell decomposition method to the residual network, we obtain a new coreness for each node, which is more accurate to indicate spreading influence of node in the original network. Our approach is applied to three real weighted networks, i.e., the international trading network, the neural network of C. elegans, and the coauthorship network of scientists. And the susceptible-infected-recovered epidemic spreading model is used to make a comparison of performance between our approach and other three k-shell methods (including the weighted degree decomposition method, the s-core decomposition method, and the weighted k-shell method) in terms of four quantitative indices, i.e., the imprecision function, the standard deviation of infected fraction of max coreness node, the spreading time, and the number of recovered nodes at the end of spreading process. The experimental results show that our proposed approach is more accurate to identify the influential spreaders than the weighted degree decomposition method, the s-core decomposition method, and the weighted k-shell method, and also helps to more accurately decompose the network core structure for an optimal analysis in weighted network.
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Keywords:
- weighted networks /
- k-shell decomposition /
- redundant link /
- spreading influence
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[28] Wei B, Liu J, Wei D, Gao C, Deng Y 2015 Physica A 420 277
[29] Liu Y, Tang M, Zhou T, Do Y 2015 Sci. Rep. 5 9602
[30] Liu Y, Tang M, Zhou T, Do Y 2015 Sci. Rep. 5 13172
[31] Barrat A, Barthélemy M, Pastor-Satorras R, Vespignani A 2004 Proc. Natl. Acad. Sci. USA 101 3747
[32] Yan W, Zhou T, Wang J, Fu Z Q, Wang B H 2005 Chin. Phys. Lett. 22 510
[33] Hu H B, Wang X F 2008 Physica A 387 3769
[34] Kendall M G 1938 Biometrika 30 81
[35] Batagelj V, Zaversnik M 2003 arXiv:cs/0310049v1
[36] Lee K M, Yang J S, Kim G, Lee J, Goh K I, Kim I M 2011 Plos One 6 e18443
[37] Watts D J, Strogatz S H 1998 Nature 393 440
[38] Newman M E J 2006 Phys. Rev. E 74 036104
[39] Saramäki J, Kivelä M, Onnela J P, Kaski K, Kertész J 2007 Phys. Rev. E 75 027105
[40] Li X, Jin Y Y, Chen G R 2003 Physica A 328 287
[41] Yan G, Fu Z Q, Chen G 2008 Eur. Phys. J. B 65 591
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[1] Wang X F, Li X, Chen G R 2012 Network Science:an Introduction (Beijing:Higher Education Press) pp3-18(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3–18页]
[2] Liu H K, Zhou T 2007 Acta Phys. Sin. 56 106(in Chinese)[刘宏鲲, 周涛2007 56 106]
[3] Zhang Z K, Liu C, Zhan X X, Lu X, Zhang C X, Zhang Y C 2016 Phys. Rep. 651 1
[4] Liu C, Zhan X X, Zhang Z K, Sun G Q, Hui P M 2015 New J. Phys. 17 113045
[5] Cohen R, Erez K, Benavraham D, Havlin S 2001 Phys. Rev. Lett. 86 3682
[6] Liu J G, Lin J H, Guo Q, Zhou T 2016 Sci. Rep. 6 21380
[7] Keeling M J, Rohani P 2008 Modeling Infectious Diseases in Humans and Animals (Princeton:Princeton University Press) p366
[8] Gong K, Tang M, Hui P M, Zhang H F, Younghae D, Lai Y C 2013 Plos One 8 e83489
[9] Liu C, Zhang Z K 2014 Commun. Nonlinear Sci. 19 896
[10] Crucitti P, Latora V, Marchiori M, Rapisarda A 2004 Physica A 340 388
[11] Liu J G, Ren Z M, Guo Q, Wang B H 2013 Acta Phys. Sin. 62 178901(in Chinese)[刘建国, 任卓明, 郭强, 汪秉宏2013 62 178901]
[12] Ren X L, L L Y 2014 Chin. Sci. Bull. 59 1175(in Chinese)[任晓龙, 吕琳媛2014科学通报 59 1175]
[13] Rombach M P, Porter M A, Fowler J H, Mucha P J 2014 Siam J. Appl. Math. 74 167
[14] Bassett D S, Wymbs N F, Rombach M P, Porter M A, Mucha P J, Grafton S T 2013 Plos Comput. Biol. 9 e1003171
[15] Liu J G, Ren Z M, Guo Q, Chen D B 2014 Plos One 9 e104028
[16] Seidman S B 1983 Social Networks 5 269
[17] Kitsak M, Gallos L K, Havlin S, Liljeros F, Muchnik L, Stanley H E, Makse H A 2010 Nat. Phys. 6 888
[18] Chen D, L L, Shang M S, Zhang Y C, Zhou T 2012 Physica A 391 1777
[19] Freeman L 1977 Sociometry 40 35
[20] Zeng A, Zhang C J 2013 Phys. Lett. A 377 1031
[21] Hou B, Yao Y, Liao D 2012 Physica A 391 4012
[22] Liu J G, Ren Z M, Guo Q 2013 Physica A 392 4154
[23] Hu Q C, Yin Y S, Ma P F, Gao Y, Zhang Y, Xing C X 2013 Acta Phys. Sin. 62 140101(in Chinese)[胡庆成, 尹龑燊, 马鹏斐, 高旸, 张勇, 邢春晓2013 62 140101]
[24] Ren Z M, Liu J G, Shao F, Hu Z L, Guo Q 2013 Acta Phys. Sin. 62 108902(in Chinese)[任卓明, 刘建国, 邵凤, 胡兆龙, 郭强2013 62 108902]
[25] Cao J X, Dong D, Xu S, Zheng X, Liu B, Luo J Z 2015 Chin. J. Comput. 38 238(in Chinese)[曹玖新, 董丹, 徐顺, 郑啸, 刘波, 罗军舟2015计算机学报 38 238]
[26] Garas A, Schweitzer F, Havlin S 2012 New J. Phys. 14 83030
[27] Eidsaa M, Almaas E 2013 Phys. Rev. E 88 062819
[28] Wei B, Liu J, Wei D, Gao C, Deng Y 2015 Physica A 420 277
[29] Liu Y, Tang M, Zhou T, Do Y 2015 Sci. Rep. 5 9602
[30] Liu Y, Tang M, Zhou T, Do Y 2015 Sci. Rep. 5 13172
[31] Barrat A, Barthélemy M, Pastor-Satorras R, Vespignani A 2004 Proc. Natl. Acad. Sci. USA 101 3747
[32] Yan W, Zhou T, Wang J, Fu Z Q, Wang B H 2005 Chin. Phys. Lett. 22 510
[33] Hu H B, Wang X F 2008 Physica A 387 3769
[34] Kendall M G 1938 Biometrika 30 81
[35] Batagelj V, Zaversnik M 2003 arXiv:cs/0310049v1
[36] Lee K M, Yang J S, Kim G, Lee J, Goh K I, Kim I M 2011 Plos One 6 e18443
[37] Watts D J, Strogatz S H 1998 Nature 393 440
[38] Newman M E J 2006 Phys. Rev. E 74 036104
[39] Saramäki J, Kivelä M, Onnela J P, Kaski K, Kertész J 2007 Phys. Rev. E 75 027105
[40] Li X, Jin Y Y, Chen G R 2003 Physica A 328 287
[41] Yan G, Fu Z Q, Chen G 2008 Eur. Phys. J. B 65 591
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