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在复杂网络的研究中, 如何有效地衡量节点的重要性一直都是学者们关心的问题. 在节点重要性研究领域, 基于拓扑学信息来判断节点重要性的方法被大量提出, 如K-shell方法. K-shell是一种寻找可能具有重要影响力节点的有效方法, 在大量的研究工作中被广泛引用. 但是, K-shell过多地强调了中心节点的影响力, 却忽视了处于网络外围节点作用力的影响. 为了更好地衡量网络中各个节点对传播的促进作用, 本文提出了一种基于迭代因子和节点信息熵的改进方法来评估各个层次节点的传播能力. 为评价本文方法的性能, 本文采用SIR模型进行仿真实验来对各节点的传播效率进行评估, 并在实验中将本文算法和其他算法进行了对比. 实验结果表明, 本文所提方法具有更好的性能, 并且适合解决大规模复杂网络中的节点重要性评价问题.In the study of complex networks, researchers have long focused on the identification of influencing nodes. Based on topological information, several quantitative methods of determining the importance of nodes are proposed. K-shell is an efficient way to find potentially affected nodes. However, the K-shell overemphasizes the influence of the location of the central nodebut ignores the effect of the force of the nodes located at the periphery of the network. Furthermore, the topology of real networks is complex, which makes the computation of the K-shell problem for large scale-free networks extremely difficult. In order to avoid ignoring the contribution of any node in the network to the propagation, this work proposes an improved method based on the iteration factor and information entropy to estimate the propagation capability of each layer of nodes. This method not only achieves the accuracy of node ordering, but also effectively avoids the phenomenon of rich clubs. To evaluate the performance of this method, the SIR model is used to simulate the propagation efficiency of each node, and the algorithm is compared with other algorithms. Experimental results show that this method has better performance than other methods and is suitable for large-scale networks.
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ks Node E 3 1 0.9571 4 0.8565 5 0.8099 2 0.7151 3 0.6366 2 7/8/9 0.4861 6 0.4374 1 21 0.6675 10 0.4034 23 0.3720 20/22/24/25/26 0.2420 11/12/13/14/16 0.1992 15 0.1733 17/18/19 0.1435 
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Iteration Node E+ 7 5 1.3728 6 1 1.4579 4 1.4378 2 1.2159 3 1.0589 5 7/8 0.7839 4 6 0.7189 9 0.6430 3 21 0.8084 2 10 0.4818 23 0.3720 1 16 0.3400 15 0.3139 20/22/24/25/26 0.2420 17 0.2219 11/12/13/14 0.1992 18/19 0.1435 下载:
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IE+算法伪代码 输入: 网络结构G=(V,E) 输出: 网络中节点的排序索引Rank 1: 通过G= (V,E)得出邻接矩阵A 2: 通过K-shell算法得出每个节点的ks值 3: IT ← 1 4: while |V| do 5:Vtemp←{ } 6:Vi.k← $\displaystyle\sum\nolimits_{j = 1}^N { {a_{ij} } }$ 7: mindegree ← min(V.k) 8: Vtemp← find (V.k== mindegree) 9: whileVtempdo 10: Vtemp. IT←IT 11:Vtemp.e+←$ -{\sum }_{j\in \varGamma \left(i\right)}{I}_{j}\cdot {\rm{ln}}{I}_{j}\cdot {\rm{k}}{{\rm{s}}}_{j} $ 12: endwhile 13: delete(Vtemp) 14: IT←IT+1 15:V←V-Vtemp 16: endwhile 17: ITMax ← IT 18: while length(Rank) <Ndo 19: for IT←ITMax to 1 do 20:Vtemp= find(max(V.IT.e+)) 21: if length (Vtemp) > 1 22: 按节点序号从大到小排序 23: end if 24: Rank ← {Vtemp, Rank} 25: end for 26: end while 27: return Rank 下载:
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Rank DC CC ks Cnc Cnc+ IKS IE+ 1 21 1 1—5 4, 5 1 1 5 2 1, 4, 5, 10 4 6—9 1 4, 5 7 1 3 2, 3 5 10—26 2 2 21 8 4 6—9, 23 21 3 3 4 7 5 11—20 7, 8 21 6—8 9 6 6 22, 24—26 6 6—8 9, 21 10 21 7 9 10 16 5 10 8 23 9 23 8 16 9 16, 20, 22, 24—26 15, 16, 23 15 23 4 10 17 10, 20, 22, 24—26 2 9 11 others 6 23 12 26 15 13 3 2 14 20, 22, 24, 25 20, 22, 24—262 15 11—13, 14, 16 3 16 15 17 17 17—19 11—14 18 18, 19 下载:
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Network N |E| $\langle d \rangle$ c $ \langle k \rangle $ βth βc NS 379 914 6.0419 0.7981 4.8232 0.1247 0.2494 EEC 986 16064 2.5869 0.4505 32.5842 0.0134 0.0268 PB 1222 16714 2.7375 0.3600 27.3552 0.0123 0.0246 Fecebook 4039 88234 3.6925 0.6170 43.6910 0.0094 0.0188 WV 7066 100736 3.2475 0.2090 28.5129 0.0069 0.0138 Sport 13866 86858 4.2748 0.2761 12.5281 0.0260 0.0520 Sex 15810 38540 7.4630 0 4.8754 0.0365 0.0730 CondMat 23122 93497 5.3523 0.6334 8.0835 0.0450 0.0900 下载:
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Network DC CC Cnc Cnc+ ks IKS IE+ NS 0.4593 0.3829 0.5604 0.7074 0.4643 0.7301 0.8958 EEC 0.8584 0.8238 0.8999 0.8771 0.8754 0.8963 0.9017 PB 0.8443 0.7956 0.8771 0.8667 0.8653 0.8859 0.9465 Facebook 0.6255 0.4948 0.7416 0.8614 0.6773 0.8926 0.9364 WV 0.8022 0.8583 0.8992 0.8939 0.9171 0.8981 0.9661 Sport 0.6909 0.6891 0.7875 0.8025 0.7437 0.8583 0.9197 Sex 0.4119 0.7329 0.7623 0.8283 0.5151 0.8065 0.8174 CondMat 0.5912 0.7268 0.7303 0.8114 0.6464 0.8565 0.9254 下载:
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Network M(DC) M(CC) M(Cnc) M(Cnc+) M(ks) M(IKS) M(IE+) NS 0.7642 0.9927 0.9302 0.9593 0.6428 0.8286 0.9221 EEC 0.9571 0.9828 0.9748 0.9998 0.9216 0.9328 0.9881 PB 0.9328 0.9301 0.9433 0.9586 0.9063 0.9266 0.9721 Facebook 0.9398 0.9667 0.9355 0.9646 0.9419 0.9457 0.9898 Sport 0.9032 0.9534 0.9292 0.9377 0.8606 0.9137 0.9818 Sex 0.6001 0.9122 0.9332 0.9581 0.5287 0.9248 0.9989 CondMat 0.8615 0.9544 0.9871 0.9864 0.8032 0.9069 0.9996 下载:
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