Identifying spreading influence nodes for social networks
Yang OU, Qiang GUO, Jianguo LIU
Identifying spreading influence nodes for social networks
The identification of spreading influence nodes in social networks, which studies how to detect important individuals in human society, has attracted increasing attention from physical and computer science, social science and economics communities. The identification algorithms of spreading influence nodes can be used to evaluate the spreading influence, describe the node’s position, and identify interaction centralities. This review summarizes the recent progress about the identification algorithms of spreading influence nodes from the viewpoint of social networks, emphasizing the contributions from physical perspectives and approaches, including the microstructure-based algorithms, community structure-based algorithms, macrostructure-based algorithms, and machine learning-based algorithms. We introduce diffusion models and performance evaluation metrics, and outline future challenges of the identification of spreading influence nodes.
complex network / network science / spreading influence / machine learning
[1] |
Albert, R Jeong, H Barabási, A L ( 1999). Diameter of the World-Wide Web. Nature, 401( 6749): 130– 131
CrossRef
Google scholar
|
[2] |
Bae, J Kim, S ( 2014). Identifying and ranking influential spreaders in complex networks by neighborhood coreness. Physica A: Statistical Mechanics and Its Applications, 395: 549– 559
CrossRef
Google scholar
|
[3] |
Bao, Z K Liu, J G Zhang, H F ( 2017). Identifying multiple influential spreaders by a heuristic clustering algorithm. Physics Letters A, 381( 11): 976– 983
CrossRef
Google scholar
|
[4] |
Barabási, A L Albert, R ( 1999). Emergence of scaling in random networks. Science, 286( 5439): 509– 512
CrossRef
Google scholar
|
[5] |
Barabási, A L Bonabeau, E ( 2003). Scale-free networks. Scientific American, 288( 5): 60– 69
CrossRef
Google scholar
|
[6] |
Belkin, M Niyogi, P ( 2003). Laplacian eigenmaps for dimensionality reduction and data representation. Neural Computation, 15( 6): 1373– 1396
CrossRef
Google scholar
|
[7] |
Berahmand, K Bouyer, A Samadi, N ( 2018). A new centrality measure based on the negative and positive effects of clustering coefficient for identifying influential spreaders in complex networks. Chaos, Solitons, and Fractals, 110: 41– 54
CrossRef
Google scholar
|
[8] |
Bertozzi, A L Franco, E Mohler, G Short, M B Sledge, D ( 2020). The challenges of modeling and forecasting the spread of COVID-19. Proceedings of the National Academy of Sciences of the United States of America, 117( 29): 16732– 16738
CrossRef
Google scholar
|
[9] |
Boguñá, M Pastor-Satorras, R Díaz-Guilera, A Arenas, A ( 2004). Models of social networks based on social distance attachment. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 70( 5): 056122
Pubmed
|
[10] |
Bonacich, P ( 1972). Factoring and weighting approaches to status scores and clique identification. Journal of Mathematical Sociology, 2( 1): 113– 120
CrossRef
Google scholar
|
[11] |
Borge-Holthoefer J Moreno Y ( 2012). Absence of influential spreaders in rumor dynamics. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 85(2): 026116
Pubmed
|
[12] |
Brin, S Page, L ( 1998). The anatomy of a large-scale hypertextual web search engine. In: Proceedings of the 7th International Conference on World Wide Web. Brisbane: Association for Computing Machinery, 107– 117
|
[13] |
Brockmann, D Helbing, D ( 2013). The hidden geometry of complex, network-driven contagion phenomena. Science, 342( 6164): 1337– 1342
CrossRef
Google scholar
|
[14] |
Bucur, D ( 2020). Top influencers can be identified universally by combining classical centralities. Scientific Reports, 10( 1): 20550
CrossRef
Google scholar
|
[15] |
Burt, R S Kilduff, M Tasselli, S ( 2013). Social network analysis: Foundations and frontiers on advantage. Annual Review of Psychology, 64( 1): 527– 547
CrossRef
Google scholar
|
[16] |
Buyalskaya, A Gallo, M Camerer, C F ( 2021). The golden age of social science. Proceedings of the National Academy of Sciences of the United States of America, 118( 5): e2002923118
CrossRef
Google scholar
|
[17] |
Campan, A Cuzzocrea, A Truta, T M ( 2017). Fighting fake news spread in online social networks: Actual trends and future research directions. In: IEEE International Conference on Big Data. Boston, MA, 4453– 4457
|
[18] |
Cantwell G T Newman M E J ( 2019). Mixing patterns and individual differences in networks. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 99(4): 042306
Pubmed
|
[19] |
Cao Z Qin T Liu T Y Tsai M F Li H (2007). Learning to rank: From pairwise approach to listwise approach. In: Proceedings of the 24th International Conference on Machine Learning. Corvallis, OR: Association for Computing Machinery, 129– 136
|
[20] |
Chen, D B Gao, H Lü, L Zhou, T ( 2013). Identifying influential nodes in large-scale directed networks: The role of clustering. PLoS One, 8( 10): e77455
CrossRef
Google scholar
|
[21] |
Chen, D B Lü, L Y Shang, M S Zhang, Y C Zhou, T ( 2012). Identifying influential nodes in complex networks. Physica A: Statistical Mechanics and Its Applications, 391( 4): 1777– 1787
CrossRef
Google scholar
|
[22] |
Chen, D B Sun, H L Tang, Q Tian, S Z Xie, M ( 2019). Identifying influential spreaders in complex networks by propagation probability dynamics. Chaos, 29( 3): 033120
CrossRef
Google scholar
|
[23] |
Chen, J Y Zhang, J Xu, X H Fu, C B Zhang, D Zhang, Q P Xuan, Q ( 2021a). E-LSTM-D: A deep learning framework for dynamic network link prediction. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 51( 6): 3699– 3712
CrossRef
Google scholar
|
[24] |
Chen, S Ren, Z M Liu, C Zhang, Z K ( 2020). Identification methods of vital nodes on temporal network. Journal of University of Electronic Science and Technology of China, 49( 2): 291– 314 (in Chinese)
|
[25] |
Chen, W Wang, Y J Yang, S Y ( 2009). Efficient influence maximization in social networks. In: Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. Paris, 199– 208
|
[26] |
Chen, Y Guo, Q Liu, M Liu, J G ( 2021b). Improved gravity model for identifying the influential nodes. Europhysics Letters, 136( 6): 68004
CrossRef
Google scholar
|
[27] |
Chen, Y C Zhu, W Y Peng, W C Lee, W C Lee, S Y ( 2014). CIM: Community-based influence maximization in social networks. ACM Transactions on Intelligent Systems and Technology, 5( 2): 1– 31
CrossRef
Google scholar
|
[28] |
Cohen, J E ( 1992). Infectious diseases of humans: Dynamics and control. Journal of the American Medical Association, 268( 23): 3381
CrossRef
Google scholar
|
[29] |
Dai, J Y Wang, B Sheng, J F Sun, Z J Khawaja, F R Ullah, A Dejene, D A Duan, G H ( 2019). Identifying influential nodes in complex networks based on local neighbor contribution. IEEE Access, 7: 131719– 131731
CrossRef
Google scholar
|
[30] |
Dai, L Guo, Q Liu, X L Liu, J G Zhang, Y C ( 2018). Identifying online user reputation in terms of user preference. Physica A: Statistical Mechanics and Its Applications, 494: 403– 409
CrossRef
Google scholar
|
[31] |
Dong, G Wang, F Shekhtman, L M Danziger, M M Fan, J Du, R Liu, J Tian, L Stanley, H E Havlin, S ( 2021). Optimal resilience of modular interacting networks. Proceedings of the National Academy of Sciences of the United States of America, 118( 22): e1922831118
CrossRef
Google scholar
|
[32] |
Dorogovtsev, S N Goltsev, A V Mendes, J F F ( 2008). Critical phenomena in complex networks. Reviews of Modern Physics, 80( 4): 1275– 1335
CrossRef
Google scholar
|
[33] |
Fan, C Zeng, L Sun, Y Liu, Y Y ( 2020). Finding key players in complex networks through deep reinforcement learning. Nature Machine Intelligence, 2( 6): 317– 324
CrossRef
Google scholar
|
[34] |
Freeman, L C ( 1977). A set of measures of centrality based on betweenness. Sociometry, 40( 1): 35– 41
CrossRef
Google scholar
|
[35] |
Freeman, L C ( 1978). Centrality in social networks conceptual clarification. Social Networks, 1( 3): 215– 239
CrossRef
Google scholar
|
[36] |
Freeman, L C Borgatti, S P White, D R ( 1991). Centrality in valued graphs: A measure of betweenness based on network flow. Social Networks, 13( 2): 141– 154
CrossRef
Google scholar
|
[37] |
Fu, J Q Liu, M Deng, C Y Huang, J Jiang, M Z Guo, Q Liu, J G ( 2020). Spreading model of the COVID-19 based on the complex human mobility. Journal of University of Electronic Science and Technology of China, 49( 3): 383– 391 (in Chinese)
|
[38] |
Galstyan A Cohen P ( 2007). Cascading dynamics in modular networks. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 75(3): 036109
Pubmed
|
[39] |
Galvão, V Miranda, J G Andrade, R F Andrade, Jr J S Gallos, L K Makse, H A ( 2010). Modularity map of the network of human cell differentiation. Proceedings of the National Academy of Sciences of the United States of America, 107( 13): 5750– 5755
CrossRef
Google scholar
|
[40] |
Gao, S Ma, J Chen, Z M Wang, G H Xing, C M ( 2014). Ranking the spreading ability of nodes in complex networks based on local structure. Physica A: Statistical Mechanics and Its Applications, 403: 130– 147
CrossRef
Google scholar
|
[41] |
Ghalmane, Z Cherifi, C Cherifi, H Hassouni, M E ( 2019a). Centrality in complex networks with overlapping community structure. Scientific Reports, 9( 1): 10133
CrossRef
Google scholar
|
[42] |
Ghalmane, Z El Hassouni, M Cherifi, C Cherifi, H ( 2019b). Centrality in modular networks. EPJ Data Science, 8( 1): 15
CrossRef
Google scholar
|
[43] |
Girvan, M Newman, M E J ( 2002). Community structure in social and biological networks. Proceedings of the National Academy of Sciences of the United States of America, 99( 12): 7821– 7826
CrossRef
Google scholar
|
[44] |
Guimerà R Danon L Díaz-Guilera A Giralt F Arenas A ( 2003). ELF-similar community structure in a network of human interactions. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 68( 6): 065103
Pubmed
|
[45] |
Guo, C Yang, L Chen, X Chen, D Gao, H Ma, J ( 2020). Influential nodes identification in complex networks via information entropy. Entropy, 22( 2): 242– 260
CrossRef
Google scholar
|
[46] |
Guo, Q Yin, R R Liu, J G ( 2019). Node importance identification for temporal networks via the TOPSIS method. Journal of University of Electronic Science and Technology of China, 48( 2): 296– 300 (in Chinese)
|
[47] |
Halappanavar, M Sathanur, A V Nandi, A K ( 2016). Accelerating the mining of influential nodes in complex networks through community detection. In: Proceedings of the ACM International Conference on Computing Frontiers. Como, 64– 71
|
[48] |
Hall, M Frank, E Holmes, G Pfahringer, B Reutemann, P Witten, L H ( 2009). The WEKA data mining software: An update. SIGKDD Explorations, 11( 1): 10– 18
CrossRef
Google scholar
|
[49] |
Hamilton W L Ying R Leskovec J (2017). Inductive representation learning on large graphs. In: Proceedings of the 31st International Conference on Neural Information Processing Systems. Long Beach, CA: Curran Associates Inc., 1025– 1035
|
[50] |
Han, Z M Wu, Y Tan, X S Duan, D G Yang, W J ( 2015). Ranking key nodes in complex networks by considering structural holes. Acta Physica Sinica, 64( 5): 058902
CrossRef
Google scholar
|
[51] |
Hethcote, H W ( 2000). The mathematics of infectious diseases. SIAM Review, 42( 4): 599– 653
CrossRef
Google scholar
|
[52] |
Hou, L Liu, J G Pan, X Wang, B H ( 2014). A social force evacuation model with the leadership effect. Physica A: Statistical Mechanics and Its Applications, 400: 93– 99
CrossRef
Google scholar
|
[53] |
Hu, G Xu, X Zhang, W M Zhou, Y ( 2019). Contribution analysis for assessing node importance indices with principal component analysis. Acta Electronica Sinica, 47( 2): 358– 365 (in Chinese)
|
[54] |
Hu, Y Ji, S Jin, Y Feng, L Stanley, H E Havlin, S ( 2018). Local structure can identify and quantify influential global spreaders in large scale social networks. Proceedings of the National Academy of Sciences of the United States of America, 115( 29): 7468– 7472
CrossRef
Google scholar
|
[55] |
Huang, H Shen, H Meng, Z Chang, H He, H ( 2019). Community-based influence maximization for viral marketing. Applied Intelligence, 49( 6): 2137– 2150
CrossRef
Google scholar
|
[56] |
Ivanov, S Durasov, N Burnaev, E ( 2018). Learning node embeddings for influence set completion. In: IEEE International Conference on Data Mining Workshops. Singapore, 1034– 1037
|
[57] |
Jeong, H Mason, S P Barabási, A L Oltvai, Z N ( 2001). Lethality and centrality in protein networks. Nature, 411( 6833): 41– 42
CrossRef
Google scholar
|
[58] |
Jia, J S Lu, X Yuan, Y Xu, G Jia, J Christakis, N A ( 2020). Population flow drives spatio–temporal distribution of COVID-19 in China. Nature, 582( 7812): 389– 394
CrossRef
Google scholar
|
[59] |
Kempe, D Kleinberg, J Tardos, E ( 2003). Maximizing the spread of influence through a social network. In: Proceedings of the 9th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining. Washington, D.C., 137– 146
|
[60] |
Kipf T N Welling M ( 2016). Semi-supervised classification with graph convolutional networks. arXiv preprints, arXiv:1609.02907
|
[61] |
Kitsak, M Gallos, L K Havlin, S Liljeros, F Muchnik, L Stanley, H E Makse, H A ( 2010). Identification of influential spreaders in complex network. Nature Physics, 6( 11): 888– 893
CrossRef
Google scholar
|
[62] |
Kleinberg, J M ( 1999). Authoritative sources in a hyperlinked environment. Journal of the ACM, 46( 5): 604– 632
CrossRef
Google scholar
|
[63] |
Klimt, B Yang, Y ( 2004). The Enron Corpus: A new dataset for email classification research. In: Proceedings of the 15th European Conference on Machine Learning. Berlin: Springer, 217– 226
|
[64] |
Knight, W R ( 1966). A computer method for calculating Kendall’s τ with un-grouped data. Journal of the American Statistical Association, 61( 314): 436– 439
CrossRef
Google scholar
|
[65] |
Kumar, A Snyder, M ( 2002). Protein complexes take the bait. Nature, 415( 6868): 123– 124
CrossRef
Google scholar
|
[66] |
Kumar, S Panda, B S ( 2020). Identifying influential nodes in social networks: Neighborhood coreness based voting approach. Physica A: Statistical Mechanics and Its Applications, 553: 124215
CrossRef
Google scholar
|
[67] |
Kunegis, J ( 2016). KONECT: The Koblenz network collection. In: Proceedings of the 22nd International Conference on World Wide Web. Rio de Janeiro: Association for Computing Machinery, 1343– 1350
|
[68] |
Leskovec, J Kleinberg, J Faloutsos, C ( 2007). Graph evolution: Densification and shrinking diameters. ACM Transactions on Knowledge Discovery from Data, 1( 1): 2
CrossRef
Google scholar
|
[69] |
Leskovec, J Lang, K J Dasgupta, A Mahoney, M W ( 2009). Community structure in large networks: Natural cluster sizes and the absence of large well-defined clusters. Internet Mathematics, 6( 1): 29– 123
CrossRef
Google scholar
|
[70] |
Liben-Nowell, D L Kleinberg, J ( 2007). The link-prediction problem for social networks. Journal of the American Society for Information Science and Technology, 58( 7): 1019– 1031
CrossRef
Google scholar
|
[71] |
Li, C Wang, L Sun, S W Xia, C Y ( 2018). Identification of influential spreaders based on classified neighbors in real-world complex networks. Applied Mathematics and Computation, 320: 512– 523
CrossRef
Google scholar
|
[72] |
Li H Bhowmick S S Sun A X ( 2013). CINEMA: Conformity-aware greedy algorithm for influence maximization in online social networks. In: Proceedings of the 16th International Conference on Extending Database Technology. Genoa: Association for Computing Machinery, 323– 334
|
[73] |
Li, Q Zhou, T Lü, L Y Chen, D B ( 2014). Identifying influential spreaders by weighted LeaderRank. Physica A: Statistical Mechanics and Its Applications, 404: 47– 55
CrossRef
Google scholar
|
[74] |
Li, Z Ren, T Ma, X Liu, S Zhang, Y Zhou, T ( 2019). Identifying influential spreaders by gravity model. Scientific Reports, 9( 1): 8387
CrossRef
Google scholar
|
[75] |
Lin, J ( 1991). Divergence measures based on the Shannon entropy. IEEE Transactions on Information Theory, 37( 1): 145– 151
CrossRef
Google scholar
|
[76] |
Lin, J H Guo, Q Dong, W Z Tang, L Y Liu, J G ( 2014). Identifying node spreading influence with largest k-core values. Physics Letters A, 378( 45): 3279– 3284
CrossRef
Google scholar
|
[77] |
Liu, J G Lin, J H Guo, Q Zhou, T ( 2016a). Locating influential nodes via dynamics-sensitive centrality. Scientific Reports, 6( 1): 21380
CrossRef
Google scholar
|
[78] |
Liu, J G Ren, Z M Guo, Q ( 2013a). Ranking the spreading influence in complex networks. Physica A: Statistical Mechanics and Its Applications, 392( 18): 4154– 4159
CrossRef
Google scholar
|
[79] |
Liu, J G Ren, Z M Guo, Q Wang, B H ( 2013b). Node importance ranking of complex networks. Acta Physica Sinica, 62( 17): 178901
CrossRef
Google scholar
|
[80] |
Liu, J G Wang, Z Y Guo, Q Guo, L Chen, Q Ni, Y Z ( 2017a). Identifying multiple influential spreaders via local structural similarity. Europhysics Letters, 119( 1): 18001
CrossRef
Google scholar
|
[81] |
Liu, J Q Li, X R Dong, J C ( 2021). A survey on network node ranking algorithms: Representative methods, extensions, and applications. Science China Technological Sciences, 64( 3): 451– 461
CrossRef
Google scholar
|
[82] |
Liu, X L Liu, J G Yang, K Guo, Q Han, J T ( 2017b). Identifying online user reputation of user-object bipartite networks. Physica A: Statistical Mechanics and Its Applications, 467: 508– 516
CrossRef
Google scholar
|
[83] |
Liu, Y Tang, M Zhou, T Do, Y ( 2015a). Core-like groups result in invalidation of identifying super-spreader by k-shell decomposition. Scientific Reports, 5( 1): 9602
CrossRef
Google scholar
|
[84] |
Liu, Y Tang, M Zhou, T Do, Y ( 2015b). Improving the accuracy of the k-shell method by removing redundant links: From a perspective of spreading dynamics. Scientific Reports, 5( 1): 13172
CrossRef
Google scholar
|
[85] |
Liu, Y Tang, M Zhou, T Do, Y ( 2016b). Identify influential spreaders in complex networks, the role of neighborhood. Physica A: Statistical Mechanics and Its Applications, 452: 289– 298
CrossRef
Google scholar
|
[86] |
Liu, Z H Jiang, C Wang, J Y Yu, H ( 2015c). The node importance in actual complex networks based on a multi-attribute ranking method. Knowledge-Based Systems, 84: 56– 66
CrossRef
Google scholar
|
[87] |
Lou, T C Tang, J ( 2013). Mining structural hole spanners through information diffusion in social networks. In: Proceedings of the 22nd International Conference on World Wide Web. Rio de Janeiro: Association for Computing Machinery, 825– 836
|
[88] |
Lü, L Zhang, Y C Yeung, C H Zhou, T ( 2011). Leaders in social networks, the delicious case. PLoS One, 6( 6): e21202
CrossRef
Google scholar
|
[89] |
Lü, L Y Chen, D B Ren, X L Zhang, Q M Zhang, Y C Zhou, T ( 2016). Vital nodes identification in complex networks. Physics Reports, 650: 1– 63
CrossRef
Google scholar
|
[90] |
Lusseau, D Schneider, K Boisseau, O J Haase, P Slooten, E Dawson, S M ( 2003). The bottlenose Dolphin community of doubtful sound features a large proportion of long-lasting associations. Behavioral Ecology and Sociobiology, 54( 4): 396– 405
CrossRef
Google scholar
|
[91] |
Ma, L L Ma, C Zhang, H F Wang, B H ( 2016). Identifying influential spreaders in complex networks based on gravity formula. Physica A: Statistical Mechanics and Its Applications, 451: 205– 212
CrossRef
Google scholar
|
[92] |
Ma, S J Ren, Z M Ye, C M Guo, Q Liu, J G ( 2014). Node influence identification via resource allocation dynamics. International Journal of Modern Physics C, 25( 11): 1450065
CrossRef
Google scholar
|
[93] |
Ma, T H Liu, Q Cao, J Tian, Y Al-Dhelaan, A Al-Rodhaan, M ( 2020). LGIEM: Global and local node influence based community detection. Future Generation Computer Systems, 105: 533– 546
CrossRef
Google scholar
|
[94] |
Macqueen J (1967). Some methods for classification and analysis of multivariate observations. In: Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability. Berkeley, CA: University of California Press, 281– 297
|
[95] |
Maji, G ( 2020). Influential spreaders identification in complex networks with potential edge weight based k-shell degree neighborhood method. Journal of Computational Science, 39: 101055
CrossRef
Google scholar
|
[96] |
Maji, G Mandal, S Sen, S ( 2020). A systematic survey on influential spreaders identification in complex networks with a focus on k-shell based techniques. Expert Systems with Applications, 161: 113681
CrossRef
Google scholar
|
[97] |
Massa P Salvetti M Tomasoni D (2009). Bowling alone and trust decline in social network sites. In: Proceedings of 8th IEEE International Conference on Dependable, Autonomic and Secure Computing. Chengdu, 658– 663
|
[98] |
McAuley J Leskovec J (2012). Learning to discover social circles in ego networks. In: Proceedings of the 25th International Conference on Neural Information Processing Systems. Lake Tahoe, NV: Curran Accociates, 539– 547
|
[99] |
Moore, B ( 1981). Principal component analysis in linear systems: Controllability, observability, and model reduction. IEEE Transactions on Automatic Control, 26( 1): 17– 32
CrossRef
Google scholar
|
[100] |
Muthukrishna, M Schaller, M ( 2020). Are collectivistic cultures more prone to rapid transformation? Computational models of cross-cultural differences, social network structure, dynamic social influence, and cultural change. Personality and Social Psychology Review, 24( 2): 103– 120
CrossRef
Google scholar
|
[101] |
Namtirtha, A Dutta, A Dutta, B ( 2018). Weighted k-shell degree neighborhood method: An approach independent of completeness of global network structure for identifying the influential spreaders. In: 10th International Conference on Communication Systems & Networks. Bengaluru: IEEE, 81– 88
|
[102] |
Namtirtha, A Dutta, A Dutta, B Sundararajan, A Simmhan, Y ( 2021). Best influential spreaders identification using network global structural properties. Scientific Reports, 11( 1): 2254
CrossRef
Google scholar
|
[103] |
Nargundkar, A Rao, Y S ( 2016). InfluenceRank: A machine learning approach to measure influence of Twitter users. In: International Conference on Recent Trends in Information Technology. Chennai: IEEE, 1– 6
|
[104] |
Newman, M E J ( 2001). The structure of scientific collaboration networks. Proceedings of the National Academy of Sciences of the United States of America, 98( 2): 404– 409
CrossRef
Google scholar
|
[105] |
Newman M E J ( 2006). Finding community structure in networks using the eigenvectors of matrices. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 74( 3): 036104
Pubmed
|
[106] |
Niepert M Ahmed M Kutzkov K (2016). Learning convolutional neural networks for graphs. In: Proceedings of the 33rd International Conference on Machine Learning. New York, NY: JMLR.org, 2014– 2023
|
[107] |
Ou, Y Guo, Q Xing, J L Liu, J G ( 2022). Identification of spreading influence nodes via multi-level structural attributes based on the graph convolutional network. Expert Systems with Applications, 203: 117515
CrossRef
Google scholar
|
[108] |
Pal, S K Kundu, S Murthy, C A ( 2014). Centrality measures, upper bound, and influence maximization in large scale directed social networks. Fundamenta Informaticae, 130( 3): 317– 342
CrossRef
Google scholar
|
[109] |
Palla, G Derényi, I Farkas, I Vicsek, T ( 2005). Uncovering the overlapping community structure of complex networks in nature and society. Nature, 435( 7043): 814– 818
CrossRef
Google scholar
|
[110] |
Pan, R K Saramäki, J ( 2012). The strength of strong ties in scientific collaboration networks. Europhysics Letters, 97( 1): 18007
CrossRef
Google scholar
|
[111] |
Pan, Y Li, D H Liu, J G Liang, J Z ( 2010). Detecting community structure in complex networks via node similarity. Physica A: Statistical Mechanics and Its Applications, 389( 14): 2849– 2857
CrossRef
Google scholar
|
[112] |
Peng, C Wang, X Pei, J Zhu, W ( 2019). A survey on network embedding. IEEE Transactions on Knowledge and Data Engineering, 31( 5): 833– 852
CrossRef
Google scholar
|
[113] |
Qi, X Duval, R D Christensen, K Fuller, E Spahiu, A Wu, Q Wu, Y Tang, W Zhang, C ( 2013). Terrorist networks, network energy and node removal: A new measure of centrality based on Laplacian energy. Social Networking, 2( 1): 19– 31
CrossRef
Google scholar
|
[114] |
Qiu, L Q Jia, W Yu, J F Fan, X Gao, W W ( 2019). PHG: A three-phase algorithm for influence maximization based on community structure. IEEE Access, 7: 62511– 62522
CrossRef
Google scholar
|
[115] |
Ren, X Zhu, Y Wang, S Liao, H Han, X Lü, L ( 2015). Online social network analysis and the relation with regional economic development. Journal of University of Electronic Science and Technology of China, 44( 5): 643– 651 (in Chinese)
|
[116] |
Ren, X L Lü, L Y ( 2013). Review of ranking nodes in complex networks. Chinese Science Bulletin, 59( 13): 1175– 1197
CrossRef
Google scholar
|
[117] |
Ren, Z M ( 2020). Node influence of the dynamic networks. Acta Physica Sinica, 69( 4): 24– 32 (in Chinese)
|
[118] |
Ren, Z M Liu, J G Shao, F Hu, Z L Guo, Q ( 2013a). Analysis of the spreading influence of the nodes with minimum k-shell value in complex networks. Acta Physica Sinica, 62( 10): 108902
CrossRef
Google scholar
|
[119] |
Ren, Z M Shao, F Liu, J G Guo, Q Wang, B H ( 2013b). Node importance measurement based on the degree and clustering coefficient information. Acta Physica Sinica, 62( 12): 128901
CrossRef
Google scholar
|
[120] |
Sabidussi, G ( 1966). The centrality index of a graph. Psychometrika, 31( 4): 581– 603
CrossRef
Google scholar
|
[121] |
Sacchet, M D Prasad, G Foland-Ross, L C Thompson, P M Gotilb, I H ( 2014). Elucidating brain connectivity networks in major depressive disorder using classification-based scoring. In: 11th International Symposium on Biomedical Imaging. Beijing: IEEE, 246– 249
|
[122] |
Shang, J X Zhou, S B Li, X Liu, L C Wu, H C ( 2017). CoFIM: A community-based framework for influence maximization on large-scale networks. Knowledge-Based Systems, 117: 88– 100
CrossRef
Google scholar
|
[123] |
Shang, Q Deng, Y Cheong, K H ( 2021). Identifying influential nodes in complex networks: Effective distance gravity model. Information Sciences, 577: 162– 179
CrossRef
Google scholar
|
[124] |
Sheikhahmadi, A Nematbakhsh, M A Shokrollahi, A ( 2015). Improving detection of influential nodes in complex networks. Physica A: Statistical Mechanics and Its Applications, 436: 833– 845
CrossRef
Google scholar
|
[125] |
Silva, T C Zhao, L ( 2012). Network-based high level data classification. IEEE Transactions on Neural Networks and Learning Systems, 23( 6): 954– 970
CrossRef
Google scholar
|
[126] |
Soffer, S N Vázquez, A ( 2005). Network clustering coefficient without degree-correlation biases. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 71( 5): 057101
CrossRef
Google scholar
|
[127] |
Spring, N Mahajan, R Wetherall, D ( 2002). Measuring ISP topologies with rocketfuel. ACM SIGCOMM Computer Communication Review, 32( 4): 133– 145
CrossRef
Google scholar
|
[128] |
Su, X P Song, Y R ( 2015). Leveraging neighborhood “structural holes” to identifying key spreaders in social networks. Acta Physica Sinica, 64( 2): 020101
CrossRef
Google scholar
|
[129] |
Sun, H L Chen, D B He, J L Chng, E ( 2019). A voting approach to uncover multiple influential spreaders on weighted networks. Physica A: Statistical Mechanics and Its Applications, 519: 303– 312
CrossRef
Google scholar
|
[130] |
Tang, L Liu, H ( 2009). Relational learning via latent social dimensions. In: Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. Paris, 817– 826
|
[131] |
Tang, L Y Li, S N Lin, J H Guo, Q Liu, J G ( 2016). Community structure detection based on the neighbor node degree information. International Journal of Modern Physics C, 27( 4): 1650046
CrossRef
Google scholar
|
[132] |
Tixier, A J P Rossi, M E G Malliaros, F D Read, J Vazirgiannis, M ( 2019). Perturb and combine to identify influential spreaders in real-world networks. In: Proceedings of the IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining. Vancouver, 73– 80
|
[133] |
Tulu, M M Hou, R Younas, T ( 2018). Identifying influential nodes based on community structure to speed up the dissemination of information in complex network. IEEE Access, 6: 7390– 7401
CrossRef
Google scholar
|
[134] |
Ullah, A Wang, B Sheng, J Long, J Khan, N Sun, Z ( 2021). Identification of nodes influence based on global structure model in complex networks. Scientific Reports, 11( 1): 6173
CrossRef
Google scholar
|
[135] |
Wang, F She, J Ohyama, Y Wu, M ( 2019). Deep-learning-based identification of influential spreaders in online social networks. In: IECON 45th Annual Conference of the IEEE Industrial Electronics Society. Lisbon, 6854– 6858
|
[136] |
Wang, Y Cong, G Song, G J Xie, K Q ( 2010). Community-based greedy algorithm for mining top-k influential nodes in mobile social networks. In: Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. Washington, D.C., 1039– 1048
|
[137] |
Wang Y F Yan G H Ma Q Q Wu Y Zhang M (2018). Identifying influential nodes based on vital communities. In: 16th International Conference on Dependable, Autonomic and Secure Computing, 16th International Conference on Pervasive Intelligence and Computing, 4th International Conference on Big Data Intelligence and Computing and Cyber Science and Technology Congress. Athens: IEEE, 314– 317
|
[138] |
Wang, Z X Zhao, Y Xi, J K Du, C J ( 2016). Fast ranking influential nodes in complex networks using a k-shell iteration factor. Physica A: Statistical Mechanics and Its Applications, 461: 171– 181
CrossRef
Google scholar
|
[139] |
Watts, D J Dodds, P S ( 2007). Influential, networks, and public opinion formation. Journal of Consumer Research, 34( 4): 441– 458
CrossRef
Google scholar
|
[140] |
Watts, D J Strogatz, S H ( 1998). Collective dynamics of “small-world” networks. Nature, 393( 6684): 440– 442
CrossRef
Google scholar
|
[141] |
Wei, H Pan, Z Hu, G Zhang, L Yang, H Li, X Zhou, X ( 2018). Identifying influential nodes based on network representation learning in complex networks. PLoS One, 13( 7): e0200091
CrossRef
Google scholar
|
[142] |
Wu, Z Pan, S Chen, F Long, G Zhang, C Yu, P S ( 2021). A comprehensive survey on graph neural networks. IEEE Transactions on Neural Networks and Learning Systems, 32( 1): 4– 24
CrossRef
Google scholar
|
[143] |
Xie N ( 2006). Social Network Analysis of Blogs. Dissertation for the Master’s Degree. Bristol: University of Bristol
|
[144] |
Yan, S Tang, S T Pei, S S Jiang, J Zhang, X Ding, W R Zheng, M Z ( 2013). The spreading of opposite opinions on online social networks with authoritative nodes. Physica A: Statistical Mechanics and Its Applications, 392( 17): 3846– 3855
CrossRef
Google scholar
|
[145] |
Yan, X L Cui, Y P Ni, S J ( 2020). Identifying influential spreaders in complex networks based on entropy weight method and gravity law. Chinese Physics B, 29( 4): 048902
CrossRef
Google scholar
|
[146] |
Yang, J Leskovec, J ( 2012). Defining and evaluating network communities based on ground-truth. In: Proceedings of the ACM SIGKDD Workshop on Mining Data Semantics. Beijing, 1– 8
|
[147] |
Yang, J Leskovec, J ( 2013). Overlapping community detection at scale: A nonnegative matrix factorization approach. In: Proceedings of the 6th ACM International Conference on Web Search and Data Mining. Rome, 587– 596
|
[148] |
Yang, J N Liu, J G Guo, Q ( 2018a). Node importance identification for temporal network based on inter-layer similarity. Acta Physica Sinica, 67( 4): 279– 286 (in Chinese)
|
[149] |
Yang, K Guo, Q Liu, J G ( 2018b). Community detection via measuring the strength between nodes for dynamics networks. Physica A: Statistical Mechanics and Its Applications, 509: 256– 264
CrossRef
Google scholar
|
[150] |
Yang, X H Xiong, S ( 2021). Identification of node influence using network representation learning in complex network. Journal of Chinese Computer Systems, 42( 2): 418– 423 (in Chinese)
|
[151] |
Yang, Y Z Wang, X Chen, Y Hu, M Ruan, C W ( 2020). A novel centrality of influential nodes identification in complex networks. IEEE Access, 8: 58742– 58751
CrossRef
Google scholar
|
[152] |
Yin, R R Guo, Q Yang, J N Liu, J G ( 2018). Inter-layer similarity-based eigenvector centrality measures for temporal networks. Physica A: Statistical Mechanics and Its Applications, 512: 165– 173
CrossRef
Google scholar
|
[153] |
Yu, E Y Wang, Y P Fu, Y Chen, D B Xie, M ( 2020). Identifying critical nodes in complex networks via graph convolutional networks. Knowledge-Based Systems, 198: 105893
CrossRef
Google scholar
|
[154] |
Yu, S B Gao, L Xu, L D Gao, Z Y ( 2019). Identifying influential spreaders based on indirect spreading in neighborhood. Physica A: Statistical Mechanics and Its Applications, 523: 418– 425
CrossRef
Google scholar
|
[155] |
Zachary, W W ( 1977). An information flow model for conflict and fission in small groups. Journal of Anthropological Research, 33( 4): 452– 473
CrossRef
Google scholar
|
[156] |
Zareie, A Sheikhahmadi, A Jalili, M ( 2019). Influential node ranking in social networks based on neighborhood diversity. Future Generation Computer Systems, 94: 120– 129
CrossRef
Google scholar
|
[157] |
Zeng, A C Zhang, J ( 2013). Ranking spreaders by decomposing complex networks. Physics Letters A, 377( 14): 1031– 1035
CrossRef
Google scholar
|
[158] |
Zhang, D Wang, Y Zhang, Z ( 2019a). Identifying and quantifying potential super-spreaders in social networks. Scientific Reports, 9( 1): 14811
CrossRef
Google scholar
|
[159] |
Zhang, J X Chen, D B Dong, Q Zhao, Z D ( 2016). Identifying a set of influential spreaders in complex networks. Scientific Reports, 6( 1): 27823
CrossRef
Google scholar
|
[160] |
Zhang, M H Chen, Y X ( 2018). Link prediction based on graph neural networks. In: Proceedings of the 32nd International Conference on Neural Information Processing Systems. Montreal: Curran Associates Inc., 5171– 5181
|
[161] |
Zhang, W Yang, J Ding, X Y Zou, X M Han, H Y Zhao, Q C ( 2019b). Groups make nodes powerful: Identifying influential nodes in social networks based on social conformity theory and community features. Expert Systems with Applications, 125: 249– 258
CrossRef
Google scholar
|
[162] |
Zhao, G H Jia, P Huang, C Zhou, A Fang, Y ( 2020a). A machine learning based framework for identifying influential nodes in complex networks. IEEE Access, 8: 65462– 65471
CrossRef
Google scholar
|
[163] |
Zhao, G H Jia, P Zhou, A Zhang, B ( 2020b). InfGCN: Identifying influential nodes in complex networks with graph convolutional networks. Neurocomputing, 414: 18– 26
CrossRef
Google scholar
|
[164] |
Zhao, X Y Huang, B Tang, M Zhang, H F Chen, D B ( 2014a). Identifying effective multiple spreaders by coloring complex networks. Europhysics Letters, 108( 6): 68005
CrossRef
Google scholar
|
[165] |
Zhao, Z J Guo, Q Yu, K Liu, J G ( 2020c). Identifying influential nodes for the networks with community structure. Physica A: Statistical Mechanics and Its Applications, 551: 123893
CrossRef
Google scholar
|
[166] |
Zhao, Z Y Yu, H Zhu, Z L Wang, X F ( 2014b). Identifying influential spreaders based on network community structure. Chinese Journal of Computers, 37( 4): 753– 766 (in Chinese)
|
[167] |
Zhao, Z Y Wang, X F Zhang, W Zhu, Z L ( 2015). A community-based approach to identifying influential spreaders. Entropy, 17( 4): 2228– 2252
CrossRef
Google scholar
|
[168] |
Zhou, M Y Xiong, W M Wu, X Y Zhang, Y X Liao, H ( 2018). Overlapping influence inspires the selection of multiple spreaders in complex networks. Physica A: Statistical Mechanics and Its Applications, 508: 76– 83
CrossRef
Google scholar
|
[169] |
Zhou, T Lü, L Y Zhang, Y C ( 2009). Predicting missing links via local information. European Physical Journal B, 71( 4): 623– 630
CrossRef
Google scholar
|
/
〈 | 〉 |