Abstract
Network motifs are patterns of over-represented node interactions in a network which have been previously used as building blocks to understand various aspects of the social networks. In this paper, we use motif patterns to characterize the information diffusion process in social networks. We study the lifecycle of information cascades to understand what leads to saturation of growth in terms of cascade reshares, thereby resulting in expiration, an event we call “diffusion inhibition”. In an attempt to understand what causes inhibition, we use motifs to dissect the network obtained from information cascades coupled with traces of historical diffusion or social network links. Our main results follow from experiments on a dataset of cascades from the Weibo platform and the Flixster movie ratings. We observe the temporal counts of 5-node undirected motifs from the cascade temporal networks leading to the inhibition stage. Empirical evidences from the analysis lead us to conclude the following about stages preceding inhibition: (1) individuals tend to adopt information more from users they have known in the past through social networks or previous interactions thereby creating patterns containing triads more frequently than acyclic patterns with linear chains and (2) users need multiple exposures or rounds of social reinforcement for them to adopt an information and as a result information starts spreading slowly thereby leading to the death of the cascade. Following these observations, we use motif-based features to predict the edge cardinality of the network exhibited at the time of inhibition. We test features of motif patterns using regression models for both individual patterns and their combination and we find that motifs as features are better predictors of the future network organization than individual node centralities.
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References
Alon Uri (2007) Network motifs: theory and experimental approaches. Nat Rev Genet 8:450–461
Sarajlic O, Yaveroglu A, Malod-Dognin N, Przulj N (2016) Graphlet-based characterization of directed networks. Sci Rep 6:35098
Babai László, Luks Eugene M (1983) Canonical labeling of graphs. In: Proceedings of the Fifteenth Annual ACM Symposium on Theory of Computing, STOC ’83, pp 171–183, New York, NY, USA
Bao Q, Cheung William K, Liu J (2016) Inferring motif-based diffusion models for social networks. In: Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence, IJCAI 2016, New York, NY, USA, 9–15 July 2016, pp 3677–3683
Benson Austin R, Gleich David F, Leskovec Jure (2016) Higher-order organization of complex networks. Science 353(6295):163–166
Berlusconi Giulia, Calderoni Francesco, Parolini Nicola, Verani Marco, Piccardi Carlo (2016) Link prediction in criminal networks: a tool for criminal intelligence analysis. PLOS One 11:04
Björklund Andreas, Husfeldt Thore, Kaski Petteri, Koivisto Mikko (2012) The traveling salesman problem in bounded degree graphs. ACM Trans Algorithms 8(2):18:1–18:13
Chakraborty T, Ganguly N, Mukherjee A (2015) An author is known by the context she keeps: significance of network motifs in scientific collaborations. Soc Netw Anal Mining 5(1):16
Cheng J, Adamic L, Dow PA, Kleinberg JM, Leskovec J (2014) Can cascades be predicted? In: Proceedings of the 23rd International Conference on World Wide Web, WWW ’14, pp 925–936, New York, NY, USA
Cheng J, Adamic LA, Kleinberg JM, Leskovec J (2016) Do cascades recur? In: Proceedings of the 25th International Conference on World Wide Web, WWW ’16
Ciriello Giovanni, Guerra Concettina (2008) A review on models and algorithms for motif discovery in protein protein interaction networks. Briefings Fun Genom 7(2):147
Cui P, Jin S, Yu L, Wang F, Zhu W, Yang S (2013) Cascading outbreak prediction in networks: A data-driven approach. In: Proceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD ’13, pp 901–909, New York, NY, USA
David Easley, Jon Kleinberg (2010) Networks, crowds, and markets: reasoning about a highly connected world. Cambridge University Press, New York
Vicario Michela Del, Bessi Alessandro, Zollo Fabiana, Petroni Fabio, Scala Antonio, Caldarelli Guido, Stanley H Eugene, Quattrociocchi Walter (2016) The spreading of misinformation online. Proc Natl Acad Sci 113(3):554–559
Derényi Imre, Palla Gergely, Vicsek Tamás (2005) Clique percolation in random networks. Phys Rev Lett 94:160202
Domingos P (2005) Mining social networks for viral marketing. IEEE Intell Syst 20(1):80–82
Dorogovtsev SN, Goltsev AV, Mendes JFF (2006) \(k\)-core organization of complex networks. Phys Rev Lett 96:040601
Farajtabar M, Wang Y, Gomez-Rodriguez M, Li S, Zha H, Song L (2015) Coevolve: a joint point process model for information diffusion and network co-evolution. In: Cortes C, Lawrence ND, Lee DD, Sugiyama M, Garnett R (eds) Advances in Neural Information Processing Systems 28, pp 1945–1953
Fire M, Tenenboim L, Lesser O, Puzis R, Rokach L, Elovici Y (2011) Link prediction in social networks using computationally efficient topological features. In: 2011 IEEE Third International Conference on Privacy, Security, Risk and Trust and 2011 IEEE Third International Conference on Social Computing
Gallos L, Havlin S, Kitsak M, Liljeros F, Makse H, Muchnik L, Stanley H (2010) Identification of influential spreaders in complex networks. Nat Phys 6(11):888–893
Goel S, Watts DJ, Goldstein DG (2012) The structure of online diffusion networks. In: Proceedings of the 13th ACM conference on electronic commerce, pp 623–638
Gomez-Rodriguez M, Balduzzi D, Schölkopf B (2011) Uncovering the temporal dynamics of diffusion networks. In: Proceedings of the 28th International Conference on Machine Learning, ICML 2011, Bellevue, Washington, USA, June 28–July 2, 2011, pp 561–568
Gomez Rodriguez M, Leskovec J, Krause A (2010) Inferring networks of diffusion and influence. In: Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD ’10, New York, NY, USA
Guo Ruocheng, Shaabani Elham, Bhatnagar Abhinav, Shakarian Paulo (2016) Toward early and order-of-magnitude cascade prediction in social networks. Soc Netw Anal Mining 6(1):64:1–64:18
Hocevar Tomaz, Demsar Janez (2014) A combinatorial approach to graphlet counting. Bioinformatics 30(4):559
Huang Z, Li X, Chen H (2005) Link prediction approach to collaborative filtering. In: Proceedings of the 5th ACM/IEEE-CS Joint Conference on Digital Libraries, JCDL ’05, pp 141–142, New York, NY, USA
Ingram PJ, Stumpf MPH, Stark J (2006) Network motifs: structure does not determine function. BMC Genom 7(1):108
Kang Chanhyun, Kraus Sarit, Molinaro Cristian, Spezzano Francesca, Subrahmanian VS (2016) Diffusion centrality: a paradigm to maximize spread in social networks. Artif Intell 239:70–96
Katona Zsolt, Zubcsek Peter Pal, Sarvary Miklos (2011) Network effects and personal influences: the diffusion of an online social network. J Market Res 48(3):425–443
Kempe D, Kleinberg J, Tardos E (2003) Maximizing the spread of influence through a social network. In: Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD ’03, New York, NY, USA
Kim M, Leskovec J (2011) The network completion problem: inferring missing nodes and edges in networks. In SDM, pp 47–58
Kovanen Lauri, Kaski Kimmo, Kertsz Jnos, Saramki Jari (2013) Temporal motifs reveal homophily, gender-specific patterns, and group talk in call sequences. Proc Natl Acad Sci 110(45):18070–18075
Budka M, Juszczyszyn K, Musial K (2011) Link prediction based on subgraph evolution in dynamic social networks, pp 27–34
Lahiri M, Berger-Wolf TY (2007) Structure prediction in temporal networks using frequent subgraphs
Leskovec Jure, Singh Ajit, Kleinberg Jon (2006) Patterns of influence in a recommendation network. Springer, Berlin, pp 380–389
Liben-Nowell David, Kleinberg Jon (2007) The link-prediction problem for social networks. J Am Soc Inf Sci Technol 58(7):1019–1031
Liu Kai, Cheung WK, Liu J (2013) Detecting stochastic temporal network motifs for human communication patterns analysis. In: Proceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, ASONAM ’13
Milo R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, Alon U (2002) Network motifs: simple building blocks of complex networks. Science 298(5594):824–827
Milo Ron, Itzkovitz Shalev, Kashtan Nadav, Levitt Reuven, Shen-Orr Shai, Ayzenshtat Inbal, Sheffer Michal, Alon Uri (2004) Superfamilies of evolved and designed networks. Science 303(5663):1538–1542
Moores Geoffrey, Shakarian Paulo, Macdonald Brian, Howard Nicholas (2014) Finding near-optimal groups of epidemic spreaders in a complex network. PLOS One 9:04
Ogata Yosihiko (1998) Space-time point-process models for earthquake occurrences. Annals of the Institute of Statistical Mathematics 50
Palla Gergely, Pollner Péter, Barabási Albert-László, Vicsek Tamás (2009) Social group dynamics in networks. Springer, Berlin, pp 11–38
Peixoto Tiago P (2014) The graph-tool python library. figshare
Rizoiu MA, Xie L, Sanner S, Cebrián M, Yu H, Van Hentenryck P (2017) Expecting to be hip: Hawkes intensity processes for social media popularity. In WWW
Rozenshtein P, Gionis A, Prakash BA, Vreeken J (2016) Reconstructing an epidemic over time. In Proceedings of the 22Nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD ’16, pp 1835–1844, New York, NY, USA
Sarkar Soumajyoti, Guo Ruocheng, Shakarian Paulo (2017) Understanding and forecasting lifecycle events in information cascades. Soc Netw Anal Mining 7(1):55
Andrade Jr Jos S, Zheng Z, Pei S, Muchnik L, Makse HA (2014) Searching for superspreaders of information in real-world social media. Sci Rep 4:5547
Shakarian P, Bhatnagar A, Aleali A, Shaabani E, Guo R (2015) Diffusion in social networks. pp 47–58
Shakarian P, Paulo D (2012) Large social networks can be targeted for viral marketing with small seed sets. In: Proceedings of the 2012 International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2012), ASONAM ’12, Washington, DC, USA. IEEE Computer Society
Ron Milo, Shmoolik Mangan, Uri Alon, Shen-Orr Shai S (2002) Network motifs in the transcriptional regulation network of Escherichia coli. Nat Rev Genet 31:64–68
Steeg GV, Ghosh R, Lerman K (2011) What stops social epidemics? In ICWSM. The AAAI Press
Tibshirani Robert (1994) Regression shrinkage and selection via the lasso. J R Stat Soc, Series B 58:267–288
Ullmann JR (1976) An algorithm for subgraph isomorphism. J ACM 23(1):31–42
Wernicke Sebastian (2006) Efficient detection of network motifs. IEEE/ACM Trans Comput Biol Bioinf 3(4):347–359
Wernicke Sebastian, Rasche Florian (2006) Fanmod: a tool for fast network motif detection. Bioinformatics 22(9):1152
Wong E, Baur B, Quader S, Huang CH (2012) Biological network motif detection: principles and practice. In: Briefings in Bioinformatics
Xie J, Yan W (2007) Pattern-based characterization of time series
Yang SH, Zha H (2013) Mixture of mutually exciting processes for viral diffusion. In: Proceedings of the 30th International Conference on Machine Learning, volume 28, Proceedings of Machine Learning Research, Atlanta, Georgia, USA
Yang SH, Zha H (2013) Mixture of mutually exciting processes for viral diffusion. In: Proceedings of the 30th International Conference on International Conference on Machine Learning—Volume 28, ICML’13
Yu H, Xie L, Sanner S (2015) The lifecyle of a youtube video: Phases, content and popularity. In: Proceedings of the Ninth International Conference on Web and Social Media, ICWSM 2015, University of Oxford, Oxford, UK, May 26–29, 2015, pp 533–542
Yuan Ming, Lin Yi (2006) Model selection and estimation in regression with grouped variables. J R Stat Soc, Ser B 68:49–67
Zhao Q, Erdogdu MA, He HY, Rajaraman A, Leskovec J (2015) Seismic: a self-exciting point process model for predicting tweet popularity. In Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD ’15, pp 1513–1522, New York, NY, USA
Zhao Y, Levina E, Zhu J (2011) Community extraction for social networks. Proceedings of the National Academy of Sciences 108(18)
Acknowledgements
Some of the authors are supported through the AFOSR Young Investigator Program (YIP) grant FA9550-15-1-0159, ARO grant W911NF-15-1-0282, and the DoD Minerva program grant N00014-16-1-2015.
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Sarkar, S., Guo, R. & Shakarian, P. Using network motifs to characterize temporal network evolution leading to diffusion inhibition. Soc. Netw. Anal. Min. 9, 14 (2019). https://doi.org/10.1007/s13278-019-0556-z
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DOI: https://doi.org/10.1007/s13278-019-0556-z