-
Identifying key nodes in complex networks or evaluating the relative node importance with respect to others using quantitative methods is a fundamental issue in network science. To address the limitations of existing approaches—namely the subjectivity in assigning weights to importance indicators and the insufficient integration of global and local structural information—this paper proposes an entropy-weighted multi-channel convolutional neural network framework (EMCNN). First, a parameter-free entropy-based weight allocation model is constructed to dynamically assign weights to multiple node importance indicators by computing their entropy values, thereby mitigating the subjectivity inherent in traditional parameter-setting methods and enhancing the objectivity of indicator fusion. Second, global and local structural features are decoupled and reconstructed into separate channels to form multi-channel feature maps, which significantly enhance the representational capacity of the network structure. Third, by leveraging the feature extraction capabilities of convolutional neural networks and the integration power of attention mechanisms, the framework extracts deep representations of nodes from the multi-channel feature maps, while emphasizing key structural information through attention-based weighting, thus enabling more accurate identification and characterization of node importance. To validate the effectiveness of the proposed method, extensive experiments are conducted on nine real-world networks using the SIR spreading model, assessing performance in terms of correlation, accuracy, and robustness. The Kendall correlation coefficient is employed as the primary evaluation metric to measure the consistency between predicted node importance and actual spreading influence. Additionally, experiments are performed on three representative synthetic networks to further test the model’s generalizability. Experimental results demonstrate that EMCNN consistently and effectively evaluates node influence under varying transmission rates, and significantly outperforms mainstream algorithms in both correlation and accuracy. These findings highlight the method’s strong generalization ability and broad applicability in key node identification tasks within complex networks.
-
Keywords:
- entropy /
- convolutional neural network /
- node importance
-
[1] Lü L Y, Chen D B, Ren X L, Zhang Q M, Zhang Y C, Zhou T 2016 Phys. Rep. 650 1
[2] Pastor-Satorras R, Vespignani A 2001 Phys. Rev. Lett. 86 3200
[3] Albert R, Barabási A L 2002 Rev. Modern Phys. 74 47
[4] Zeng Y 2020 Neurocomputing 416 158
[5] Albert R, Jeong H, Barabási A L 1999 Nature 401 130
[6] Lü L, Zhou T, Zhang Q M, Stanley H E 2016 Nat. Commun. 7 10168
[7] Xu X, Zhu C, Wang Q Y, Zhu X Q, Zhou Y 2020 Sci. Rep. 10 2691
[8] Brin S, Page L 1998 Computer Networks and ISDN Systems 30 107
[9] Freeman L C 1977 Sociometry 40 35
[10] Sabidussi G 1966 Psychometrika 31 581
[11] Kitsak M, Gallos L K, Havlin S, Liljeros F, Muchnik L, Stanley H E, Makse H A 2010 Nat. Phys. 6 888
[12] Bonacich P 1987 American J. Sociology 92 1170
[13] Lü L, Zhang Y C, Yeung C H, Zhou T 2011 PLoS One 6 21202
[14] Curado M, Tortosa L, Vicent J F 2023 Inform. Sciences 628 177
[15] Ullah A, Wang B, Sheng J F, Long J, Khan N, Sun Z J 2021 Expert Syst. Appl. 186 115778
[16] Liu W Z, Lu P L, Zhang T 2023 IEEE Trans. Comput. Soc. Syst. 11 2105
[17] Ruan Y R, Liu S Z, Tang J, Guo Y M, Yu T Y 2024 Expert Syst. Appl. 268 126292
[18] Rezaei A A, Munoz J, Jalili M, Khayyam H 2023 Expert Syst. Appl. 214 119086
[19] Li X Y, Zhang Z J, Liu J M, Gai K K 2019 Proceedings of the 2019 ACM International Symposium on Blockchain and Secure Critical Infrastructure New York, USA, May 9–12, 2019 p13–17
[20] Zhao G H, Jia P, Zhou A M, Zhang B 2020 Neurocomputing 414 18
[21] Yu E Y, Wang Y P, Fu Y, Chen D B, Xie M 2020 Knowl-Based Syst. 198 105893
[22] Zhang M, Wang X J, Jin L, Song M, Li Z Y 2022 Neurocomputing 497 13
[23] Wang B Y, Yang X C, Lu S R, Tang Y P, Hong S Q, Jiang H Y 2024 Acta Phys. Sin. 73 226401 (in Chinese) [王博雅, 杨小春, 卢升荣, 唐勇平, 洪树权, 蒋惠园 2024 物理学报 73 226401]
[24] Chen L Y, Xi Y, Dong L, Zhao M J, Li C L, Liu X, Cui X H 2024 Inf. Process. Manag. 61 103775
[25] Tang J X, Qu J T, Song S H, Zhao Z L, Du Q 2024 J. King Saud Univ.–Comput. Inf. Sci. 36 102183
[26] Zhang P, Wang J L, Li X J, Li M H, Di Z R, Fan Y 2008 Physica A 387 6869
[27] Zhang J X, Chen D B, Dong Q, Zhao Z D 2016 Sci. Rep. 6 27823
[28] Hajarathaiah K, Enduri M K, Dhuli S, Anamalamudi S, Cenkeramaddi L R 2023 IEEE Access 11 808
[29] Sheng J F, Dai J Y, Wang B, Duan G H, Long J, Zhang J K, Guan K R, Hu S, Chen L, Guan W H 2020 Physica A 541 123262
[30] Kermack W O, McKendrick A G 1927 Proc. R. Soc. Lond. Ser. A-Contain. Pap. Math. Phys. Charact. 115 700
[31] Bae J, Kim S 2014 Physica A 395 549–559
[32] Kendall M G 1945 Biometrika 33 239
[33] Barabási A L, Albert R 1999 Sci. 286 509
[34] Dorogovtsev S N, Goltsev A V, Mendes J F F 2006 Phys. Rev. Lett. 96 040601
[35] Blagus N, Šubelj L, Bajec M 2012 Physica A 391 2794
[36] Newman M E J 2006 Phys. Rev. E 74 036104
[37] Rual J F, Venkatesan K, Hao T, Hirozane-Kishikawa T, Dricot A, Li N, Berriz G F, Gibbons F D, Dreze M, Ayivi-Guedehoussou N et al. 2005 Nature 437 1173
[38] Jeong H, Mason S P, Barabási A L, Oltvai Z N 2001 Nature 411 41
[39] Knuth D E 1993 The Stanford GraphBase: A Platform for Combinatorial Computing New York, USA: ACM Press
[40] Gleiser P M, Danon L 2003 Adv. Complex Syst. 6 565
[41] Colizza V, Pastor-Satorras R, Vespignani A 2007 Nat. Phys. 3 276
[42] Kunegis J 2013 Proceedings of the 22nd International Conference on World Wide Web Rio de Janeiro, Brazil, May 13–17, 2013 p1343–1350
[43] Batagelj V, Mrvar A 1998 Connections 21 47
Metrics
- Abstract views: 17
- PDF Downloads: 4
- Cited By: 0
下载:
