Abstract
Identifying vital nodes in hypernetworks is of great significance for understanding the connectivity property and dynamic characteristic of the hypernetwork. A number of methods have been proposed to identify vital nodes of hypernetworks, ranging from centralities of nodes to diffusion-based processes, but most of them ignore the impacts of neighbors. Many researchers use degree, hyper-degree or the clustering coefficient to identify vital nodes. However, the degree can only take into account the neighbor size, the hyper-degree can only consider the incidence hyperedge size, regardless of the clustering property of the neighbors. The clustering coefficient could only reflect the density of connections among the neighbors and neglect the activity of the target node. In this paper, we present a novel local centrality to identify vital nodes by combining the influence of the node itself and neighbor as well as clustering coefficient information. To evaluate the performance of the proposed method, the robustness results measured by the hypernetwork efficiency through removing the vital nodes for protein complex hypernetwork show that the new method can more effective in identify vital nodes.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
All data, models, and codes generated or used during the study are available from the corresponding author upon request.
Change history
02 April 2024
This article has been retracted. Please see the Retraction Notice for more detail: https://doi.org/10.1007/s10878-024-01157-3
References
Arularasan A, Suresh A, Seerangan K (2019) Identification and classification of best spreader in the domain of interest over the social networks. Cluster Comput 22(2):4035–4045
Bae J, Kim S (2014) Identifying and ranking influential spreaders in complex networks by neighborhood coreness. Phys A Stat Mech Appl 395:549–559
Berge C (1973) Graphs and hypergraph. Elsevier, New York
Bonacich P (1972) Factoring and weighting approaches to status scores and clique identifification. J Math Sociol 2(1):113–120
Bonacich P, Lloyd P (2001) Eigenvector-like measures of centrality for asymmetric relations. Social Netw 23(3):191–201
Chen D, Lü L, Shang MS (2012) Identifying influential nodes in complex networks. Phys A Stat Mech Appl 391(4):1777–1787
Codd EF (1970) A relational model of data for large shared data banks. Commun ACM 13(6):377–387
Estrada E, Rodriguez-Velazquez J (2006) Subgraph centrality and clustering in complex hyper-networks. Phys A Stat Mech Appl 364:581–594
Freeman L (1978) Centrality in social networks conceptual clarifification. Social Netw 1:215–239
Guo JL, Zhu XY, Suo Q (2016) Non-uniform evolving hypergraphs and weighted evolving hypergraphs. Sci Rep 6(1):36648
Hu F, Zhao HX, Ma X (2013) An evolving hypernetwork model and its properties (in chinese). Sci Sin-Phys Meeh Astron 43:16–22
Hu F, Liu M, Zhao J (2018) Analysis and application of topological properties of protein complex hypernetworks. Complex Syst Complex Sci 15(4):31–38
Ibnoulouafi A, Haziti ME, Cherifi H (2018) M-centrality: identifying key nodes based on global position and local degree variation. J Stat Mech Theor Exp 2018(7):073407
Jiang W, Wei B, Zhan J, Xie C, Zhou D (2016) A visibility graph power averaging aggregation operator: a methodology based on network analysis. Comput Ind Eng 101:260–268
Jiang Y, Yang SQ, Yan YW, Tong TC, Dai JY (2022) A novel method for identifying influential nodes in complex networks based on gravity model. Chin Phys B 31(5):058903
Kitsak M, Gallos LK, Havlin S (2010) Identification of influential spreaders in complex networks. Nature Phys 6:888–893
Latora V, Marchiori M (2007) A measure of centrality based on network efficiency. New J Phys 9(6):188
Liu JB, Wang C, Wang S (2017) Zagreb indices and multiplicative zagreb indices of eulerian graphs. Bull Malays Math Sci Soc 1–12
Liu JB, Pan X (2016) Minimizing kirchhoff index among graphs with a given vertex bipartiteness. Appl Math Comput 291:84–88
Liu JB, Yu P (2016) L: complete characterization of bicyclic graphs with minimal kirchhoff index. Discret Appl Math 200:95–107
Liu L, Qi B, Li B (2020) Requirements and developing trends of electric power communication network for new services in electric internet of things. Power Syst Technol 44(8):15
Lü L, Chen D, Ren XL, Zhang QM, Zhang YC, Zhou T (2016) Vital nodes identification in complex networks. Phys Rep 650:1–63
Mo H, Gao C, Deng Y (2015) Evidential method to identify influential nodes in complex networks. J Syst Eng Electron 26(2):371–387
Newman M (2005) A measure of betweenness centrality based on random walks. Social Netw 27(1):39–54
Rouari A, Moussaoui A, Chahir Y (2021) Deep cnn-based autonomous system for safety measures in logistics transportation. Soft Comput 25:12357–12370
Shan EF, Cai L, Zeng H, Chao-Jing P (2020) The u-position value measure on centrality of hypernetworks. Oper Res Manag Sci 29(5):135–142
Song F, Heath E, Jefferson B (2021) Hypergraph models of biological networks to identify genes critical to pathogenic viral response. BMC Bioinf 22(1):287–309
Vitali S, Glattfelder J, Battiston S (2011) The network of global corporate control. PLoS ONE 6(10):e25995
Vragović I, Louis E, Díaz-Guilera A (2005) Efficiency of informational transfer in regular and complex networks. Phys Rev E 71:036122
Wang Z, Du C, Fan J, Xing Y (2017) Ranking influential nodes in social networks based on node position and neighborhood. Neurocomputing 260:466–477
Yang Y, Xu KJ, Hong C (2021) Network dynamics on the chinese air transportation multilayer network. Int J Mod Phys C 32(05):2150070
Zamora-Lpez G, Zhou C, Kurths J (2010) Cortical hubs form a module for multisensory integration on top of the hierarchy of cortical networks. Front Neuroinf 4:1
Zeng A, Zhang CJ (2013) Ranking spreaders by decomposing complex networks. Phys Lett A 377(14):1031–1035
Zhou LN, Li FX, Gong YC (2021) Identification methods of vital nodes based on k-shell in hypernetworks. Complex Syst Complex Sci 18(03):15–22
Zhou LN, Chang X, Hu F (2022) Using adjacent structure entropy to determine vital nodes of hypernetwork. Comput Eng Appl 58(8):76–82
Acknowledgements
This work was supported by the Major Achievements Transformation Project from Qinghai Province(Nos. 2020-SF-139), the State Key Laboratory of Tibetan Intelligent Information Processing and Application, the Key Laboratory of Tibetan Intelligent Information Processing and Machine Translation of Qinghai P.R.C and the Key Laboratory of Tibetan Information Processing of Ministry of Education P.R.C.
Funding
This work was funded by the Major Achievements Transformation Project from Qinghai Province (Nos. 2020-SF-139).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This article has been retracted. Please see the retraction notice for more detail: https://doi.org/10.1007/s10878-024-01157-3
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Li, F., Xu, H., Wei, L. et al. RETRACTED ARTICLE: Identifying vital nodes in hypernetwork based on local centrality. J Comb Optim 45, 32 (2023). https://doi.org/10.1007/s10878-022-00960-0
Accepted:
Published:
DOI: https://doi.org/10.1007/s10878-022-00960-0