Abstract
The notion of a core is generalized to multiway networks. To determine the multiway cores, we adapted already-known algorithms for determining the generalized cores in one-mode and two-mode networks. A new node property, node diversity has been introduced. The newly introduced notions are illustrated with their application on two real-life networks—the European airport network and the Summer Olympic medals network. For the interactive inspection of the results, their 3D layout in X3D is supported.
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Data availability
The code and data are available at: Batagelj, V (2023) GitHub/Bavla, Multiway network analysis in R. https://github.com/bavla/ibm3m.
References
Ahmed A, Batagelj V, Fu X, Hong S-H, Merrick D, Mrvar A (2007) Visualisation and analysis of the internet movie database. In: 6th International Asia-pacific symposium on visualization, IEEE, pp 17-24
Batagelj V, Mrvar A, Zaveršnik M (1999) Partitioning approach to visualization of large graphs. In: Kratochvil J (ed) Proceedings of 7th international symposium on graph drawing, 15-19 Sept 1999, Štirin Castle, Czech Republic (Lecture notes in computer science, vol. 1731). Springer, Berlin, pp 90-97
Batagelj V, Zaveršnik M (2002) Generalized cores. Ar**v. https://doi.org/10.48550/ar**v.cs/0202039
Batagelj V (2023) Analysis of multiway networks. Slides for 1327, 1329, 1333. Sredin seminar
Batagelj V, Zaveršnik M (2003) An O(m) algorithm for cores decomposition of networks. Ar**v. https://doi.org/10.48550/ar**v.cs/0310049
Batagelj V, Zaveršnik M (2011) Fast algorithms for determining (generalized) core groups in social networks. Adv Data Anal Classif 5(2):129–145
Batagelj V, Cerinšek M (2016) Temporal cores in networks. In: International conference applied statistics, September 18–21, 2016, Ribno (Bled), Slovenia
Batagelj V (2023) GitHub/Bavla, Multiway network analysis in R. https://github.com/bavla/ibm3m
Batagelj V (2020) On fractional approach to the analysis of linked networks. Scientometrics 123:621–633. https://doi.org/10.1007/s11192-020-03383-y
Batagelj V, Ferligoj A, Doreian P (2007) Indirect Blockmodeling of 3-Way Networks. In: Brito, P, Cucumel, G, Bertrand, P, de Carvalho, F (eds) Selected contributions in data analysis and classification pp 151-159, Springer https://doi.org/10.1007/978-3-540-73560-1_14
Borgatti SP, Everett MG (1992) Regular blockmodels of multiway, multimode matrices. Soc Netw 14(1–2):91–120
Cardillo A, Gómez-Gardeñes J, Zanin M, Romance M, Papo D, del Pozo F, Boccaletti S (2013) Emergence of network features from multiplexity. Sci Rep 3:1344
Cerinšek M, Batagelj V (2015) Generalized two-mode cores. Soc Netw 42:80–87
Coleman J, Katz E, Menzel H (1957) The diffusion of an innovation among physicians. Sociometry 20:253–270
de Domenico M (2023) Datasets released for reproducibility. https://manliodedomenico.com/data.php
Everett MG, Borgatti SP (2019) Partitioning multimode networks. In: Batagelj V, Ferligoj A (eds) Doreian, P Advances in network clustering and blockmodeling Wiley
Genova VG, Giordano G, Ragozini G, Vitale MP (2022) Clustering student mobility data in 3-way networks. IFCS 2022, Porto. Slides
Karp RM (1972) Reducibility among combinatorial problems. In: Miller RE, Thatcher JW (eds) Complex Comput Comput. Plenum, New York, pp 85–103
Kapferer B (1972) Strategy and transaction in an African factory. Manchester University Press, Manchester
Krackhardt D (1987) Cognitive social structures. Soc Netw 9:104–134
Lazega E (2001) The collegial phenomenon: the social mechanisms of cooperation among peers in a corporate law partnership. Oxford University Press, Oxford
Moon JW, Moser L (1965) On cliques in graphs. Israel J Math 3:23–28
rgriffin (2018) 120 years of Olympic history: athletes and results; basic bio data on athletes and medal results from Athens 1896 to Rio 2016 https://www.kaggle.com/datasets/heesoo37/120-years-of- olympic-history-athletes-and-results
Seidman SB (1983) Network structure and minimum degree. Soc Netw 5:269–287
Wasserman S, Faust K (1994) Social network analysis: methods and applications. Cambridge University Press, Cambridge
x3dom – instant 3D the HTML way! (2023) https://www.x3dom.org/
view3dscene a 3D viewer from Castle Game Engine (2023) https://castle-engine.io/view3dscene.php
Acknowledgements
We would like to thank the three anonymous reviewers for their insightful comments and suggestions and careful reading of the manuscript. We would like to thank Andreas Plesch for extending the library X3DOM (2023) with support for Anchor ’s attribute description . The computational work reported in this paper was performed using R library MWnets. The code and data are available at Github/Bavla (Batagelj 2023). This work is supported in part by the Slovenian Research Agency (research program P1-0294 and research projects J5-2557, J1-2481 and J5-4596), and prepared within the framework of the COST action CA21163 (HiTEc).
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VB wrote the main manuscript text, prepared and analyzed the data, and prepared figures.
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Batagelj, V. Cores in multiway networks. Soc. Netw. Anal. Min. 14, 122 (2024). https://doi.org/10.1007/s13278-024-01283-0
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DOI: https://doi.org/10.1007/s13278-024-01283-0