research-article

Preferential attachment in online networks: measurement and explanations

Authors:

Jérôme Kunegis,

Marcel Blattner,

Christine MoserAuthors Info & Claims

WebSci '13: Proceedings of the 5th Annual ACM Web Science Conference

Pages 205 - 214

https://doi.org/10.1145/2464464.2464514

Published: 02 May 2013 Publication History

Abstract

We perform an empirical study of the preferential attachment phenomenon in temporal networks and show that on the Web, networks follow a nonlinear preferential attachment model in which the exponent depends on the type of network considered. The classical preferential attachment model for networks by Barabási and Albert (1999) assumes a linear relationship between the number of neighbors of a node in a network and the probability of attachment. Although this assumption is widely made in Web Science and related fields, the underlying linearity is rarely measured. To fill this gap, this paper performs an empirical longitudinal (time-based) study on forty-seven diverse Web network datasets from seven network categories and including directed, undirected and bipartite networks. We show that contrary to the usual assumption, preferential attachment is nonlinear in the networks under consideration. Furthermore, we observe that the deviation from linearity is dependent on the type of network, giving sublinear attachment in certain types of networks, and superlinear attachment in others. Thus, we introduce the preferential attachment exponent β as a novel numerical network measure that can be used to discriminate different types of networks. We propose explanations for the behavior of that network measure, based on the mechanisms that underly the growth of the network in question.

References

[1]

Aiello, L. M., Barrat, A., Cattuto, C., Ruffo, G., and Schifanella, R. Link creation and profile alignment in the aNobii social network. In Int. Conf. on Social Computing (2010), 249--256.

Digital Library

[2]

Albert, R., and Barabási, A.-L. Statistical mechanics of complex networks. Reviews of Modern Physics 74, 1 (2002), 47--97.

Digital Library

[3]

Barabási, A.-L., and Albert, R. Emergence of scaling in random networks. Science 286, 5439 (1999), 509--512.

[4]

Barabási, A.-L., Jeong, H., Neda, Z., Ravasz, E., and Schubert, A. Evolution of the social network of scientific collaborations. Physica A 311, 3--4 (2002), 590--614.

[5]

Bennett, J., and Lanning, S. The Netflix Prize. In Proc. KDD Cup (2007), 3--6.

[6]

Benz, D., Hotho, A., Jäschke, R., Krause, B., Mitzlaff, F., Schmitz, C., and Stumme, G. The social bookmark and publication management system BibSonomy. The VLDB J. 19, 6 (dec 2010), 849--875.

Digital Library

[7]

Bollobás, B. Modern Graph Theory. Springer, 1998.

[8]

Brandes, U., and Lerner, J. Structural similarity: Spectral methods for relaxed blockmodeling. J. Classification 27, 3 (2010), 279--306.

Digital Library

[9]

Capocci, A., Servedio, V. D. P., Colaiori, F., Buriol, L. S., Donato, D., Leonardi, S., and Caldarelli, G. Preferential attachment in the growth of social networks: The Internet encyclopedia Wikipedia. Phys. Rev. E 74, 3 (2006), 036116.

[10]

Celma, Ò. Music Recommendation and Discovery in the Long Tail. Springer, 2010.

Digital Library

[11]

Chaintreau, A., Hui, P., Crowcroft, J., Diot, C., Gass, R., and Scott, J. Impact of human mobility on opportunistic forwarding algorithms. IEEE Trans. on Mobile Computing 6, 6 (2007), 606--620.

Digital Library

[12]

Champernowne, D. A model of income distribution. Economic Journal 63 (1953), 318--351.

[13]

Choudhury, M. D., Lin, Y.-R., Sundaram, H., Candan, K. S., Xie, L., and Kelliher, A. How does the data sampling strategy impact the discovery of information diffusion in social media? In Proc. Int. Conf. on Weblogs and Social Media (2010), 34--41.

[14]

Choudhury, M. D., Sundaram, H., John, A., and Seligmann, D. D. Social synchrony: Predicting mimicry of user actions in online social media. In Proc. Int. Conf. on Computational Science and Engineering (2009), 151--158.

Digital Library

[15]

Clauset, A., Shalizi, C. R., and Newman, M. E. J. Power-law distributions in empirical data. SIAM Rev. 51, 4 (2009), 661--703.

Digital Library

[16]

Dahlander, L., Frederiksen, L., and Rullani, F. Online communities and open innovation: Governance and symbolic value creation. Industry and Innovation 15, 2 (2008), 115--123.

[17]

Dereich, S., and Mörters, P. Random networks with sublinear preferential attachment: Degree evolutions. Electrical J. of Probability 14 (2009), 1222--1267.

[18]

Dholakiaa, U. M., Bagozzia, R. P., and Pearo, L. K. A social influence model of consumer participation in network- and small-group-based virtual communities. Int. J. of Research in Marketing 21, 3 (2004), 241--263.

[19]

Dorogovtsev, S. N., and Mendes, J. F. F. Evolution of networks. Adv. Phys. 51 (2002), 1079--1187.

[20]

Dror, G., Koenigstein, N., Koren, Y., and Weimer, M. The Yahoo! Music dataset and KDD-Cup'11. In JMLR Workshop and Conf. Proc., vol. 18 (2012), 3--18.

[21]

Eagle, N., and Pentland, A. S. Reality Mining: Sensing complex social systems. Personal Ubiquitous Computing 10, 4 (2006), 255--268.

Digital Library

[22]

Emamy, K., and Cameron, R. CiteULike: A researcher's social bookmarking service. Ariadne, 51 (2007).

[23]

Erdős, P., and Rényi, A. On random graphs I. Publ. Math. Debrecen 6 (1959), 290--297.

[24]

Faraj, S., and Johnson, S. L. Network exchange patterns in online communities. Organization Science 22, 6 (2010), 1464--1480.

Digital Library

[25]

Gabel, A., and Redner, S. Sublinear but never superlinear preferential attachment by local network growth. arXiv:1212.0518.

[26]

Gay, B., and Dousset, B. Innovation and network structural dynamics: Study of the alliance network of a major sector of the biotechnology industry. Research Policy 34, 10 (2005), 1457--1475.

[27]

Gibrat, R. Les Inegalités économiques: Applications aux inégalités des richesses, à la concentration des entreprises, aux populations des villes, aux statistiques des familles, etc., d'une loi nouvelle: la loi de l'effect proportionnel. Sirey, 1931.

[28]

GroupLens Research. MovieLens data sets. http://www.grouplens.org/node/73, October 2006.

[29]

Gulati, R., Puranam, P., and Tushman, M. Meta-organization design: Rethinking design in interorganizational and community contexts. Strategic Management J. 33 (2012), 571--586.

[30]

Gómez, V., Kaltenbrunner, A., and López, V. Statistical analysis of the social network and discussion threads in Slashdot. In Proc. Int. World Wide Web Conf. (2008), 645--654.

Digital Library

[31]

Hanaki, N., Nakajima, R., and Ogura, Y. The dynamics of R&D network in the IT industry. Research Policy 39, 3 (2010), 386--399.

[32]

Jeong, H., Néda, Z., and Barabási, A. L. Measuring preferential attachment for evolving networks. Europhysics Lett. 61, 4 (2001), 567--572.

[33]

Kapteyn, J. C., and van Uven, M. J. Skew Frequency Curves in Biology and Statistics. Hoitsema Brothers, Groningen, 1916.

[34]

Klimt, B., and Yang, Y. The Enron corpus: A new dataset for email classification research. In Proc. European Conf. on Machine Learning (2004), 217--226.

Digital Library

[35]

Krapivsky, P. L., and Krioukov, D. Scale-free networks as preasymptotic regimes of superlinear preferential attachment. Phys. Rev. E 78 (2008), 026114.

[36]

Krapivsky, P. L., and Redner, S. Organization of growing random networks. Phys. Rev. E 63 (2001), 066123.

[37]

Lemarchand, G. A. The long-term dynamics of co-authorship scientific networks: Iberoamerican countries (1973--2010). Research Policy 41, 2 (2012), 291--305.

[38]

Ley, M. The DBLP computer science bibliography: Evolution, research issues, perspectives. In Proc. Int. Symp. on String Processing and Information Retrieval (2002), 1--10.

Digital Library

[39]

Liben-Nowell, D., and Kleinberg, J. The link prediction problem for social networks. In Proc. Int. Conf. on Information and Knowledge Management (2003), 556--559.

Digital Library

[40]

Lim, E.-P., Nguyen, V.-A., Jindal, N., Liu, B., and Lauw, H. W. Detecting product review spammers using rating behaviors. In Proc. Int. Conf. on Information and Knowledge Management (2010), 939--948.

Digital Library

[41]

Lotka, A. J. The frequency distribution of scientific productivity. J. of the Washington Academy of Sciences 16, 12 (1926), 317--324.

[42]

Massa, P., and Avesani, P. Controversial users demand local trust metrics: an experimental study on epinions.com community. In Proc. American Association for Artificial Intelligence Conf. (2005), 121--126.

Digital Library

[43]

Mislove, A. Online Social Networks: Measurement, Analysis, and Applications to Distributed Information Systems. PhD thesis, Rice University, 2009.

Digital Library

[44]

Mislove, A., Koppula, H. S., Gummadi, K. P., Druschel, P., and Bhattacharjee, B. Growth of the Flickr social network. In Proc. Workshop on Online Social Networks (2008), 25--30.

Digital Library

[45]

Moser, C., Groenewegen, P., and Huysman, M. Social norms as governance mechanisms in online professional communities. In Proc. Academy of Management Meeting (2011).

[46]

Newman, M. E. J. Clustering and preferential attachment in growing networks. Phys. Rev. E 67, 5 (2002).

[47]

Newman, M. E. J. The structure and function of complex networks. SIAM Review 45, 2 (2003), 167--256.

Digital Library

[48]

Newman, M. E. J. Power laws, Pareto distributions and Zipf's law. Contemporary Phys. 46, 5 (2006), 323--351.

[49]

Oliveira, R., and Spencer, J. Connectivity transitions in networks with super-linear preferential attachment. Internet Math 2 (2005), 121--163.

[50]

O'mahony, S., and Ferraro, F. The emergence of governance in an open source community. Academy of Management J. 50, 5 (2007), 1079--1106.

[51]

Opsahl, T., and Panzarasa, P. Clustering in weighted networks. Social Networks 31, 2 (2009), 155--163.

[52]

Opsahl, T., and Panzarasa, P. Triadic closure in two-mode networks: Redefining the global and local clustering coefficients. Social Networks 34 (2011).

[53]

Pfeil, U., Zaphiris, P., and Ang, C. S. Cultural differences in collaborative authoring of Wikipedia. J. of Computer-mediated Communication 12, 1 (2006), 88--113.

[54]

Rocha, L. E. C., Liljeros, F., and Holme, P. Information dynamics shape the sexual networks of Internet-mediated prostitution. Proc. of the National Academy of Sciences 107, 13 (2010), 5706--5711.

[55]

Rudas, A., Tóth, B., and Valkó, B. Random trees and general branching processes. Random Struct. Algorithms 31, 2 (2007), 186--202.

Digital Library

[56]

Said, A., De Luca, E. W., and Albayrak, S. How social relationships affect user similarities. In Proc. IUI Workshop on Social Recommender Systems (2010).

[57]

Simon, H. A. On a class of skew distribution functions. Biometrika 42 (1955), 425--440.

[58]

Stack Exchange Inc. Stack Exchange Data Explorer. http://data.stackexchange.com/, 2011.

[59]

Tremayne, M., Zheng, N., Lee, J. K., and Jeong, J. Issue publics on the Web: Applying network theory to the war blogosphere. J. of Computer-mediated Communication 12, 1 (2006), 290--310.

[60]

Viswanath, B., Mislove, A., Cha, M., and Gummadi, K. P. On the evolution of user interaction in Facebook. In Proc. Workshop on Online Social Networks (2009), 37--42.

Digital Library

[61]

Wagner, C. S., and Leydesdorff, L. Network structure, self-organization, and the growth of international collaboration in science. Research Policy 34, 10 (2005), 1608--1618.

[62]

Wang, E. S. T., and Chen, L. S. L. Forming relationship commitments to online communities: The role of social motivations. Computers in Human Behavior 28, 2 (2012), 570--575.

Digital Library

[63]

Watts, D. J. The 'new' science of networks. Annual Review of Sociology 30 (2004), 243--270.

[64]

Wikimedia Foundation. Wikimedia downloads. http://dumps.wikimedia.org/, January 2010.

[65]

Yule, G. U. A mathematical theory of evolution, based on the conclusions of Dr. J. C. Willis, F. R. S. Philos. Trans. of the Royal Society of London, Ser. B 213 (1925), 21--87.

[66]

Zhou, T. Understanding online community user participation: a social influence perspective. Internet Research 21, 1 (2011), 67--81.

[67]

Zipf, G. K. The Psychobiology of Language. Houghton Mifflin, 1935.

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Index Terms

Preferential attachment in online networks: measurement and explanations
1. Information systems
  1. Information systems applications

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cover image ACM Conferences

WebSci '13: Proceedings of the 5th Annual ACM Web Science Conference

May 2013

481 pages

ISBN:9781450318891

DOI:10.1145/2464464

Conference Chairs:
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University of Southampton
,
Harry Halpin
World Wide Web Consortium
,
Alex Pentland,
Program Chairs:
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Lada Adamic,
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