Abstract
Inferring tie strengths in social networks is an essential task in social network analysis. Common approaches classify the ties as weak and strong ties based on the strong triadic closure (STC). The STC states that if for three nodes, A, B, and C, there are strong ties between A and B, as well as A and C, there has to be a (weak or strong) tie between B and C. So far, most works discuss the STC in static networks. However, modern large-scale social networks are usually highly dynamic, providing user contacts and communications as streams of edge updates. Temporal networks capture these dynamics. To apply the STC to temporal networks, we first generalize the STC and introduce a weighted version such that empirical a priori knowledge given in the form of edge weights is respected by the STC. The weighted STC is hard to compute, and our main contribution is an efficient 2-approximative streaming algorithm for the weighted STC in temporal networks. As a technical contribution, we introduce a fully dynamic 2-approximation for the minimum weight vertex cover problem, which is a crucial component of our streaming algorithm. Our evaluation shows that the weighted STC leads to solutions that capture the a priori knowledge given by the edge weights better than the non-weighted STC. Moreover, we show that our streaming algorithm efficiently approximates the weighted STC in large-scale social networks.
Giuseppe F. Italiano is partially supported by MUR, the Italian Ministry for University and Research, under PRIN Project AHeAD (Efficient Algorithms for HArnessing Networked Data).
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Notes
- 1.
We use WeightedMinSTC for the decision and the optimization problem in the following if the context is clear.
References
Adriaens, F., De Bie, T., Gionis, A., Lijffijt, J., Matakos, A., Rozenshtein, P.: Relaxing the strong triadic closure problem for edge strength inference. Data Min. Knowl. Disc. 34, 1–41 (2020)
Ahmadian, S., Haddadan, S.: A theoretical analysis of graph evolution caused by triadic closure and algorithmic implications. In: International Conference on Big Data (Big Data), pp. 5–14. IEEE (2020)
Bhattacharya, S., Henzinger, M., Italiano, G.F.: Deterministic fully dynamic data structures for vertex cover and matching. J. Comput. 47(3), 859–887 (2018)
Candia, J., González, M.C., Wang, P., Schoenharl, T., Madey, G., Barabási, A.L.: Uncovering individual and collective human dynamics from mobile phone records. J. Phys. A Math. Theor. 41(22), 224015 (2008)
Chen, J., Molter, H., Sorge, M., Suchý, O.: Cluster editing in multi-layer and temporal graphs. In: International Symposium on Algorithms and Computation, ISAAC, LIPIcs, vol. 123, pp. 24:1–24:13. Schloss Dagstuhl-LZI (2018)
Easley, D.A., Kleinberg, J.M.: Networks, Crowds, and Markets - Reasoning About a Highly Connected World. Cambridge University Press, Cambridge (2010)
Eckmann, J.P., Moses, E., Sergi, D.: Entropy of dialogues creates coherent structures in e-mail traffic. Proc. Natl. Acad. Sci. 101(40), 14333–14337 (2004)
Gallai, T.: Transitiv orientierbare graphen. Acta M. Hung. 18(1–2), 25–66 (1967)
Génois, M., Barrat, A.: Can co-location be used as a proxy for face-to-face contacts? EPJ Data Sci. 7(1), 11 (2018)
Gilbert, E., Karahalios, K.: Predicting tie strength with social media. In: Proceedings of the 27th International Conference on Human Factors in Computing Systems, CHI, pp. 211–220. ACM (2009)
Gilbert, E., Karahalios, K., Sandvig, C.: The network in the garden: an empirical analysis of social media in rural life. In: Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, pp. 1603–1612 (2008)
Granovetter, M.S.: The strength of weak ties. A. J. Soc. 78(6), 1360–1380 (1973)
Grüttemeier, N., Komusiewicz, C.: On the relation of strong triadic closure and cluster deletion. Algorithmica 82, 853–880 (2020)
Hanneke, S., **ng, E.P.: Discrete temporal models of social networks. In: Airoldi, E., Blei, D.M., Fienberg, S.E., Goldenberg, A., **ng, E.P., Zheng, A.X. (eds.) ICML 2006. LNCS, vol. 4503, pp. 115–125. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-73133-7_9
Hessel, J., Tan, C., Lee, L.: Science, askscience, and badscience: on the coexistence of highly related communities. In: Proceedings of the International AAAI Conference on Web and Social Media, vol. 10, pp. 171–180 (2016)
Himmel, A., Molter, H., Niedermeier, R., Sorge, M.: Adapting the bron-kerbosch algorithm for enumerating maximal cliques in temporal graphs. Soc. Netw. Anal. Min. 7(1), 35:1–35:16 (2017)
Holme, P., Edling, C.R., Liljeros, F.: Structure and time evolution of an internet dating community. Social Netw. 26(2), 155–174 (2004)
Holme, P., Saramäki, J.: Temporal networks. Phys. Rep. 519(3), 97–125 (2012)
Huang, H., Tang, J., Wu, S., Liu, L., Fu, X.: Mining triadic closure patterns in social networks. In: International Conference on World Wide Web, WWW, pp. 499–504. ACM (2014)
Kahanda, I., Neville, J.: Using transactional information to predict link strength in online social networks. In: Proceedings of the International AAAI Conference on Web and Social Media, vol. 3, pp. 74–81 (2009)
Kempe, D., Kleinberg, J.M., Kumar, A.: Connectivity and inference problems for temporal networks. J. Comput. Syst. Sci. 64(4), 820–842 (2002)
Kleinberg, J., Tardos, E.: Algorithm Design. Pearson Education, Noida (2006)
Klimt, B., Yang, Y.: The enron corpus: a new dataset for email classification research. In: Boulicaut, J.-F., Esposito, F., Giannotti, F., Pedreschi, D. (eds.) ECML 2004. LNCS (LNAI), vol. 3201, pp. 217–226. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30115-8_22
Konstantinidis, A.L., Nikolopoulos, S.D., Papadopoulos, C.: Strong triadic closure in cographs and graphs of low maximum degree. Theor. Comp. Sci. 740, 76–84 (2018)
Konstantinidis, A.L., Papadopoulos, C.: Maximizing the strong triadic closure in split graphs and proper interval graphs. Disc. Appl. Math. 285, 79–95 (2020)
Kossinets, G., Watts, D.J.: Empirical analysis of an evolving social network. Science 311(5757), 88–90 (2006)
Latapy, M., Viard, T., Magnien, C.: Stream graphs and link streams for the modeling of interactions over time. Soc. Netw. Anal. Min. 8(1), 61:1–61:29 (2018)
Lin, N., Dayton, P.W., Greenwald, P.: Analyzing the instrumental use of relations in the context of social structure. Sociol. Meth. Res. 7(2), 149–166 (1978)
Matakos, A., Gionis, A.: Strengthening ties towards a highly-connected world. Data Min. Knowl. Disc. 36(1), 448–476 (2022)
Mislove, A., Marcon, M., Gummadi, K.P., Druschel, P., Bhattacharjee, B.: Measurement and analysis of online social networks. In: Proceedings of the 7th ACM SIGCOMM Conference on Internet Measurement, pp. 29–42 (2007)
Moinet, A., Starnini, M., Pastor-Satorras, R.: Burstiness and aging in social temporal networks. Phys. Rev. Lett. 114(10), 108701 (2015)
Oettershagen, L., Konstantinidis, A.L., Italiano, G.F.: Inferring tie strength in temporal networks (2022). https://arxiv.org/abs/2206.11705
Oettershagen, L., Kriege, N.M., Morris, C., Mutzel, P.: Classifying dissemination processes in temporal graphs. Big Data 8(5), 363–378 (2020)
Ozella, L., et al.: Using wearable proximity sensors to characterize social contact patterns in a village of rural malawi. EPJ Data Sci. 10(1), 46 (2021)
Paranjape, A., Benson, A.R., Leskovec, J.: Motifs in temporal networks. In: Proceedings of the tenth ACM International Conference on Web Search and Data Mining, pp. 601–610 (2017)
Pyatkin, A., Lykhovyd, E., Butenko, S.: The maximum number of induced open triangles in graphs of a given order. Optim. Lett. 13(8), 1927–1935 (2019)
Rossi, R.A., Ahmed, N.K.: The network data repository with interactive graph analytics and visualization. In: AAAI (2015). https://networkrepository.com/
Rozenshtein, P., Tatti, N., Gionis, A.: Inferring the strength of social ties: a community-driven approach. In: Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1017–1025. ACM (2017)
Sintos, S., Tsaparas, P.: Using strong triadic closure to characterize ties in social networks. In: Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1466–1475 (2014)
Stehlé, J., et al.: High-resolution measurements of face-to-face contact patterns in a primary school. PloS One 6(8), e23176 (2011)
Tantipathananandh, C., Berger-Wolf, T.Y.: Finding communities in dynamic social networks. In: International Conference on Data Mining, ICDM, pp. 1236–1241. IEEE (2011)
Wei, H.T., Hon, W.K., Horn, P., Liao, C.S., Sadakane, K.: An O(1)-approximation algorithm for dynamic weighted vertex cover with soft capacity. In: Approximation, Random, and Combinatorial Optics Algorithm and Techniques (APPROX/RANDOM 2018). LIPIcs, vol. 116, pp. 27:1–27:14. Schloss Dagstuhl-LZI (2018)
Wu, B., Yi, K., Li, Z.: Counting triangles in large graphs by random sampling. IEEE Trans. Knowl. Data Eng. 28(8), 2013–2026 (2016)
**ang, R., Neville, J., Rogati, M.: Modeling relationship strength in online social networks. In: International Conference on World Wide Web, WWW, pp. 981–990. ACM (2010)
Zhou, L., Yang, Y., Ren, X., Wu, F., Zhuang, Y.: Dynamic network embedding by modeling triadic closure process. In: Proceedings of the Thirty-Second AAAI Conference on Artificial Intelligence, pp. 571–578. AAAI Press (2018)
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Oettershagen, L., Konstantinidis, A.L., Italiano, G.F. (2023). Inferring Tie Strength in Temporal Networks. In: Amini, MR., Canu, S., Fischer, A., Guns, T., Kralj Novak, P., Tsoumakas, G. (eds) Machine Learning and Knowledge Discovery in Databases. ECML PKDD 2022. Lecture Notes in Computer Science(), vol 13714. Springer, Cham. https://doi.org/10.1007/978-3-031-26390-3_5
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