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A model for dynamic communicators

Published online by Cambridge University Press:  26 July 2012

ALEXANDER V. MANTZARIS and
DESMOND J. HIGHAM
ALEXANDER V. MANTZARIS
Affiliation:
Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, UK e-mail: d.j.higham@strath.ac.uk
DESMOND J. HIGHAM
Affiliation:
Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, UK e-mail: d.j.higham@strath.ac.uk
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Abstract

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We develop and test an intuitively simple dynamic network model to describe the type of time-varying connectivity structure present in many technological settings. The model assumes that nodes have an inherent hierarchy governing the emergence of new connections. This idea draws on newly established concepts in online human behaviour concerning the existence of discussion catalysts, who initiate long threads, and online leaders, who trigger feedback. We show that the model captures an important property found in e-mail and voice call data – ‘dynamic communicators’ with sufficient foresight or impact to generate effective links and having an influence that is grossly underestimated by static measures based on snaphots or aggregated data.

Keywords

Social networksComplex networksStochastic models

Information

Type
Papers
Information
European Journal of Applied Mathematics , Volume 23 , Issue 6 , December 2012, pp. 659 - 668
Copyright
Copyright © Cambridge University Press 2012

References

[1]Bajardi, P., Barrat, A., Natale, F., Savini, L. & Colizza, V. (2011) Dynamical patterns of cattle trade movements. PLoS ONE 6, e19869.CrossRefGoogle ScholarPubMed
[2]Barabási, A.-L. (2005) The origin of bursts and heavy tails in human dynamics. Nature 435, 207–211.Google Scholar
[3]Bassett, D. S., Wymbs, N. F., Porter, M.A., Mucha, P. J., Carlson, J. M. & Grafton, S. T. (2011) Dynamic reconfiguration of human brain networks during learning. Proc. Natl. Acad. Sci. USA 118, 7641–7646.CrossRefGoogle Scholar
[4]Berman, K. (1996) Vulnerability of scheduled networks and a generalization of Menger's theorem. Networks 28, 125–134.Google Scholar
[5]Coles, N. (2001) It's not what you know—it's who you know that counts. Analysing serious crime groups as social networks. Br. J. Criminol. 41, 580–594.CrossRefGoogle Scholar
[6]Eagle, N., Pentland, A. S. & Lazer, D. (2009) Inferring friendship network structure by using mobile phone data. Proc. Natl. Acad. Sci. USA 106, 15274–15278.CrossRefGoogle ScholarPubMed
[7]Esfandiar, P., Bonchi, F., Gleich, D., Greif, C., Lakshmanan, L. & On, B.-W. (2010) Fast Katz and commuters: Efficient estimation of social relatedness in large networks In: Kumar, R. & Sivakumar, D. (editors), Algorithms and Models for the Web-Graph, vol. 6516 of Lecture Notes in Computer Science, Springer, Berlin, Heidelberg, pp. 132–145.Google Scholar
[8]Gautreau, A., Barrat, A. & Barthelemy, M. (2009) Microdynamics in stationary complex networks. Proc. Natl. Acad. Sci. USA 106, 8847–8852.CrossRefGoogle ScholarPubMed
[9]Gleave, E., Welser, H. T., Lento, T. M. & Smith, M. A. (2009) A conceptual and operational definition of ‘social role’ in online community. In: Proceedings of the 42nd Hawaii International Conference on System Sciences, Los Alamitos, CA, USA, IEEE Computer Society, pp. 1–11.Google Scholar
[10]Grindrod, P. & Higham, D. J. (2010) Evolving graphs: Dynamical models, inverse problems and propagation. Proc. Roy. Soc. A 466, 753–770.Google Scholar
[11]Grindrod, P., Higham, D. J., Parsons, M. C. & Estrada, E. (2011) Communicability across evolving networks. Phys. Rev. E 83, 046120.Google Scholar
[12]Holme, P. (2005) Network reachability of real-world contact sequences. Phys. Rev. E, 71, 046119.Google Scholar
[13]Holme, P. & Saramäki, J. Temporal networks. Phys. Rep., [online] URL: http://www.sciencedirect.com/science/article/pii/S0370157312000841.Google Scholar
[14]Huffaker, D. (2010) Dimensions of leadership and social influence in online communities. Hum. Commun. Res. 36, 593–617.CrossRefGoogle Scholar
[15]Huffaker, D., Wang, J. A., Treem, J., Ahmad, M. A., Fullerton, L., Williams, D., Poole, M. S. & Contractor, N. (2009) The social behaviors of experts in massive multiplayer online role-playing games. IEEE Int. Conf. Comput. Sci. Eng. 4, 326–331.Google Scholar
[16]Isella, L., Romano, M., Barrat, A., Cattuto, C., Colizza, V., Van den Broeck, W., Gesualdo, F., Pandolfi, E., Rav, L., Rizzo, C. & Tozzi, A. E. (2011) Close encounters in a pediatric ward: Measuring face-to-face proximity and mixing patterns with wearable sensors. PLoS ONE 6, e17144.Google Scholar
[17]Katz, L. (1953) A new index derived from sociometric data analysis. Psychometrika 18, 39–43.CrossRefGoogle Scholar
[18]Kempe, D., Kleinberg, J. & Kumar, A. (2002) Connectivity and inference problems for temporal networks. J. Comput. Syst. Sci. 64, 820–842.CrossRefGoogle Scholar
[19]Kossinets, G., Kleinberg, J. & Watts, D. (2008) The structure of information pathways in a social communication network. In: Proceeding of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD'08, New York, USA, ACM, pp. 435–443.Google Scholar
[20]Kumpula, J. M., Onnela, J. P., Saramäki, J., Kaski, K. & Kertész, J. (2007) Emergence of communities in weighted networks. Phys. Rev. Lett. 99, 228701.Google Scholar
[21]Leskovec, J., Krause, A., Guestrin, C., Faloutsos, C., VanBriesen, J. & Glance, N. (August 2007) Cost-effective outbreak detection in networks. In: ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 420–429.Google Scholar
[22]Lu, Z., Savas, B., Tang, W. & Dhillon, I. (December 2010) Supervised link prediction using multiple sources. In: Data Mining (ICDM), 2010 IEEE 10th International Conference on, pp. 923–928.Google Scholar
[23]McNamara, L., Mascolo, C. & Capra, L. (September 2008) Media sharing based on colocation prediction in urban transport. In: Proceedings of ACM 14th International Conference on Mobile Computing and Networking (Mobicom08), San Francisco, CA, pp. 58–69.Google Scholar
[24]Mucha, P. J., Richardson, T., Macon, K., Porter, M. A. & Onnela, J.-P. (2010) Community structure in time-dependent, multiscale, and multiplex networks. Science 328, 876–878.Google Scholar
[25]Muchnik, L., Itzhak, R., Solomon, S. & Louzoun, Y. (2007) Self-emergence of knowledge trees: Extraction of wikipedia hierarchies. Phy. Rev. E 76, 016106.Google ScholarPubMed
[26]Newman, M. E. J. (2010) Networks an Introduction, Oxford University Press, Oxford.Google Scholar
[27]Tang, J., Musolesi, M., Mascolo, C. & Latora, V. (2009) Temporal distance metrics for social network analysis. In: Proceedings of the 2nd ACM SIGCOMM Workshop on Online Social Networks (WOSN09), Barcelona, Spain.Google Scholar
[28]Tang, J., Musolesi, M., Mascolo, C. & Latora, V. (2010) Characterising temporal distance and reachability in mobile and online social networks. SIGCOMM Comput. Commun. Rev. 40, 118–124.Google Scholar
[29]Tang, J., Musolesi, M., Mascolo, C., Latora, V. & Nicosia, V. (2010) Analysing information flows and key mediators through temporal centrality metrics. In: SNS'10: Proceedings of the 3rd Workshop on Social Network Systems, New York, USA, ACM, pp. 1–6.Google Scholar
[30]Tang, J., Scellato, S., Musolesi, M., Mascolo, C. & Latora, V. (2010) Small-world behavior in time-varying graphs. Phys. Rev. E 81, 05510.Google Scholar
[31]Zhao, K., Stehlé, J., Bianconi, G. & Barrat, A. (2011) Social network dynamics of face-to-face interactions. Phys. Rev. E 83, 056109.Google Scholar