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Social networks: Evolving graphs with memory dependent edges

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  • Grindrod, Peter
  • Parsons, Mark

Abstract

The plethora of digital communication technologies, and their mass take up, has resulted in a wealth of interest in social network data collection and analysis in recent years. Within many such networks the interactions are transient: thus those networks evolve over time. In this paper we introduce a class of models for such networks using evolving graphs with memory dependent edges, which may appear and disappear according to their recent history. We consider time discrete and time continuous variants of the model. We consider the long term asymptotic behaviour as a function of parameters controlling the memory dependence. In particular we show that such networks may continue evolving forever, or else may quench and become static (containing immortal and/or extinct edges). This depends on the existence or otherwise of certain infinite products and series involving age dependent model parameters. We show how to differentiate between the alternatives based on a finite set of observations. To test these ideas we show how model parameters may be calibrated based on limited samples of time dependent data, and we apply these concepts to three real networks: summary data on mobile phone use from a developing region; online social-business network data from China; and disaggregated mobile phone communications data from a reality mining experiment in the US. In each case we show that there is evidence for memory dependent dynamics, such as that embodied within the class of models proposed here.

Suggested Citation

  • Grindrod, Peter & Parsons, Mark, 2011. "Social networks: Evolving graphs with memory dependent edges," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3970-3981.
  • Handle: RePEc:eee:phsmap:v:390:y:2011:i:21:p:3970-3981
    DOI: 10.1016/j.physa.2011.06.015
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    Citations

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    Cited by:

    1. Han, Dun & Sun, Mei, 2014. "Can memory and conformism resolve the vaccination dilemma?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 95-104.
    2. Shen, Yi, 2013. "Detect local communities in networks with an outside rate coefficient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(12), pages 2821-2829.
    3. Desmarais, B.A. & Cranmer, S.J., 2012. "Statistical mechanics of networks: Estimation and uncertainty," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1865-1876.

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