Abstract
Finding structural similarities in graph data, like social networks, is a far-ranging task in data mining and knowledge discovery. A (conceptually) simple reduction would be to compute the automorphism group of a graph. However, this approach is ineffective in data mining since real world data does not exhibit enough structural regularity. Here we step in with a novel approach based on mappings that preserve the maximal cliques. For this we exploit the well known correspondence between bipartite graphs and the data structure formal context (G, M, I) from Formal Concept Analysis. From there we utilize the notion of clone items. The investigation of these is still an open problem to which we add new insights with this work. Furthermore, we produce a substantial experimental investigation of real world data. We conclude with demonstrating the generalization of clone items to permutations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
- 2.
This work is noted to be submitted (e.g., in [7]), but has never been published.
- 3.
The second way yields the dual context \(\mathbb {K}(H)=(W,U,I)\).
References
Borchmann, D., Hanika, T.: Individuality in social networks. In: Missaoui, R., Kuznetsov, S.O., Obiedkov, S. (eds.) Formal Concept Analysis of Social Networks, pp. 19–40. Springer International Publishing, Cham (2017). https://doi.org/10.1007/978-3-319-64167-6_2
Borchmann, D., Hanika, T.: Some experimental results on randomly generating formal contexts. In: Huchard, M., Kuznetsov, S. (eds.) CLA. CEUR Workshop Proceedings, vol. 1624, pp. 57–69. CEUR-WS.org (2016)
Club membership network dataset – KONECT, January 2016
Faulkner, R.R.: Music on Demand: Composers and Careers in the Hollywood Film Industry. Composers and Careers in the Hollywood Film Industry. Transaction Publishers, New Brunswick (2003)
Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Heidelberg (1999). https://doi.org/10.1007/978-3-642-59830-2. pp. x+284
Gleiser, P., Danon, L.: Community structure in jazz. Adv. Complex Syst. 6, 565 (2003)
Gély, A., Medina, R., Nourine, L., Renaud, Y.: Uncovering and reducing hidden combinatorics in Guigues-Duquenne bases. In: Ganter, B., Godin, R. (eds.) ICFCA 2005. LNCS (LNAI), vol. 3403, pp. 235–248. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-32262-7_16
Leskovec, J., Huttenlocher, D., Kleinberg. J.: Signed networks in social media. In: Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, pp. 1361–1370. ACM (2010)
Lichman, M.: UCI Machine Learning Repository (2013)
Lusseau, D., et al.: The bottlenose dolphin community of Doubtful Sound features a large proportion of long-lasting associations. Behav. Ecol. Sociobiol. 54(4), 396–405 (2003)
Macko, J.: On open problem – semantics of the clone items. In: Domenach, F., Ignatov, D.I., Poelmans, J. (eds.) Contributions to the 10th International Conference on Formal Concept Analysis (ICFCA 2012). CEUR Workshop Proceedings, vol. 876, pp. 130–144. CEUR-WS.org (2012)
Mangasarian, O.L., Wolberg, W.H.: Cancer diagnosis via linear programming. SIAM News 23(5), 1–18 (1990)
Medina, R., Nourine, L., Raynaud, O.: Interactive association rules discovery. In: Missaoui, R., Schmidt, J. (eds.) ICFCA 2006. LNCS (LNAI), vol. 3874, pp. 177–190. Springer, Heidelberg (2006). https://doi.org/10.1007/11671404_12
Medina, R., et al.: Efficient algorithms for clone items detection. In: CLA 2005, pp. 70–81 (2005)
Opsahl, T., Panzarasa, P.: Clustering in weighted networks. Soc. Netw. 31(2), 155–163 (2009)
Rossi, R.A., Ahmed, N.K.: The network data repository with interactive graph analytics and visualization. In: Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence (2015)
Wasserman, S., Faust, K.: Social Network Analysis. Methods and Applications. Structural Analysis in the Social Sciences. Cambridge University Press, New York (1994)
Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered Sets, pp. 445–470. Springer, Dordrecht (1982). https://doi.org/10.1007/978-94-009-7798-3_15
Acknowledgments
This work was funded by the German Federal Ministry of Education and Research (BMBF) in its program “Forschung zu den Karrierebedingungen und Karriereentwicklungen des Wissenschaftlichen Nachwuchses (FoWiN)” under Grant 16FWN016.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Doerfel, S., Hanika, T., Stumme, G. (2018). Clones in Graphs. In: Ceci, M., Japkowicz, N., Liu, J., Papadopoulos, G., Raś, Z. (eds) Foundations of Intelligent Systems. ISMIS 2018. Lecture Notes in Computer Science(), vol 11177. Springer, Cham. https://doi.org/10.1007/978-3-030-01851-1_6
Download citation
DOI: https://doi.org/10.1007/978-3-030-01851-1_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-01850-4
Online ISBN: 978-3-030-01851-1
eBook Packages: Computer ScienceComputer Science (R0)