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Inverse network sampling to explore online brand allegiance


Within the online media universe, there are many underlying communities. These may be defined, for example, through politics, location, health, occupation, extracurricular interests or retail habits. Government departments, charities and commercial organisations can benefit greatly from insights about the structure of these communities; the move to customer-centred practices requires knowledge of the customer base. Motivated by this issue, we address the fundamental question of whether a sub-network looks like a collection of individuals who have effectively been picked at random from the whole, or instead forms a distinctive community with a new, discernible structure. In the former case, to spread a message to the intended user base it may be best to use traditional broadcast media (TV, billboard), whereas in the latter case a more targeted approach could be more effective. In this work, we therefore formalise a concept of testing for sub-structure and apply it to social interaction data. First, we develop a statistical test to determine whether a given sub-network (induced sub-graph) is likely to have been generated by sampling nodes from the full network uniformly at random. This tackles an interesting inverse alternative to the more widely studied “forward” problem. We then apply the test to a Twitter reciprocated mentions network where a range of brand name based sub-networks are created via tweet content. We correlate the computed results against the independent views of 16 digital marketing professionals. We conclude that there is great potential for social media based analytics to quantify, compare and interpret online brand allegiances systematically, in real time and at large scale.

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Submitted to the European Journal of Applied Mathematics, Special Issue on Networks.

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[1] Aral S. (2012) Social science: Poked to vote. Nature 489, 212214.
[2] Aral S. & Walker D. (2012) Identifying influential and susceptible members of social networks. Science 337, 337341.
[3] Bakshy E., Hofman J. M., Mason W. A. & Watts D. J. (2011) Everyone's an influencer: Quantifying influence on Twitter. In Proceedings of the 4th ACM International Conference on Web Search and Data Mining, WSDM '11, New York, NY, USA, 2011, ACM, pp. 65–74.
[4] Bakshy E., Rosenn I., Marlow C. & Adamic L. (2012) The role of social networks in information diffusion. In Proceedings of the 21st International Conference on World Wide Web, WWW '12, New York, NY, USA, 2012, ACM, pp. 519–528.
[5] Boutet A., Kim H. & Yoneki E. (2013) Whats in Twitter, I know what parties are popular and who you are supporting now! Soc. Netw. Anal. Min. 3, 13791391.
[6] Brodie R. J., Ilic A., Juric B. & Hollebeek L. (2013) Consumer engagement in a virtual brand community: An exploratory analysis. J. Bus. Res. 66, 105114.
[7] Chana K. W. & Lib S. Y. (2010) Understanding consumer-to-consumer interactions in virtual communities: The salience of reciprocity. J. Bus. Res. 63, 10331040.
[8] Chua J., Arce-Urrizab M., Cebollada-Calvoc J.-J. & Chintaguntad P. K. (2010) An empirical analysis of shopping behavior across online and offline channels for grocery products: The moderating effects of household and product characteristics. J. Interact. Mark. 24, 251268.
[9] Ciulla F., Mocanu D., Baronchelli A., Gonçalves B., Perra N. & Vespignani A. (2012) Beating the news using social media: The case study of American Idol. EPJ Data Sci. 1, 111.
[10] Danaher P. J., Wilson I. W. & Davis R. A. (2003) A comparison of online and offline consumer brand loyalty. Mark. Sci. 22, 461476.
[11] Farhi P. (2013) Oreo's Tweeted ad was Super Bowl blackout's Big Winner, Washington Post, (February 05).
[12] Feld S. L. (1991) Why your friends have more friends than you do. Am. J. Sociol. 96, 14641477.
[13] García-Herranz M., Moro E., Cebrián M., Christakis N. A. & Fowler J. H. (2014) Using friends as sensors to detect global-scale contagious outbreaks. PLOS ONE 9 (4), e92413.
[14] Grindrod P. (2014) Mathematical Underpinnings of Analytics: Theory and Applications, Oxford University Press, Oxford.
[15] Kuehn C., Martens E. A. & Romero D. M. (2014) Critical transitions in social network activity. J. Complex Netw. 2, 141152.
[16] Kwak H., Lee C., Park H. & Moon S. (2010) What is Twitter, a social network or a news media? In Proceedings of the 19th International Conference on World Wide Web, WWW '10, New York, NY, USA, 2010, ACM, pp. 591–600.
[17] Laflin P., Mantzaris A. V., Ainley F., Otley A., Grindrod P. & Higham D. J. (2013) Discovering and validating influence in a dynamic online social network. Soc. Netw. Anal. Min. 3, 13111323.
[18] Laflin P., Mantzaris A. V., Ainley F., Otley A., Grindrod P. & Higham D. J. (2015) Anticipating activity in social media spikes. In Proceedings of the Workshop on Modelling and Mining Temporal Interactions Workshop of the 9th International Conference on the Web and Social Media, Oxford, CA, USA, 2015, Association for the Association for the Advancement of Artificial Intelligence.
[19] Laroche M., Habibi M. R. & Richard M.-O. (2013) To be or not to be in social media: How brand loyalty is affected by social media? Int. J. Inform. Manage. 33, 7682.
[20] Laroche M., Habibi M. R., Richard M.-O. & Sankaranarayanan R. (2012) The effects of social media based brand communities on brand community markers, value creation practices, brand trust and brand loyalty. Comput. Human Behav. 28, 17551767.
[21] Lazer D., Pentland A., Adamic L., Aral S., Barabási A.-L., Brewer D., Christakis N., Contractor N., Fowler J., Gutmann M. & Jebara T. (2009) Computational social science. Science 323, 721723.
[22] Lee S. H., Kim P.-J. & Jeong H. (2006) Statistical properties of sampled networks. Phys. Rev. E 73, 016102.
[23] Leskovec J. & Faloutsos C. (2006) Sampling from large graphs. In Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD '06, New York, NY, USA, 2006, ACM, pp. 631–636.
[24] Lowcay C., Marsland S. & McCartin C. (2014) Network parameters and heuristics in practice: A case study using the target set selection problem. J. Complex Netw. 2, 373393.
[25] Maiya A. S. & Berger-wolf T. Y. (2011) Benefits of bias: Towards better characterization of network sampling. In Proc. of the 17th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD '11), San Diego, 2011.
[26] Stumpf M., Wiuf C. & May R. (2005) Subnets of scale-free networks are not scale-free: Sampling properties of networks. Proc. Nat. Acad. Sci. 102, 42214224.
[27] Wu S., Hofman J. M., Mason W. A. & Watts D. J. (2011) Who says what to whom on Twitter. In Proceedings of the 20th International Conference on World wide web, WWW '11, New York, NY, USA, 2011, ACM, pp. 705–714.
[28] Zaglia M. E. (2013) Brand communities embedded in social networks. J. Bus. Res. 66, 216223.
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European Journal of Applied Mathematics
  • ISSN: 0956-7925
  • EISSN: 1469-4425
  • URL: /core/journals/european-journal-of-applied-mathematics
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