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A Temporal Network Version of Watts’s Cascade Model

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Temporal Networks

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

Threshold models of cascades in the social and economical sciences explain the spread of opinion and innovation as an effect of social influence. In threshold cascade models, fads or innovation spread between agents as determined by their interactions to other agents and their personal threshold of resistance. Typically, these models do not account for structure in the timing of interaction between the units. In this work, we extend a model of social cascades by Duncan Watts to temporal interaction networks. In our model, we assume agents are influenced by their friends and acquaintances at certain time into the past. That is, the influence of the past ages and becomes unimportant. Thus, our modified cascade model has an effective time window of influence. We explore two types of thresholds—thresholds to fractions of the neighbors, or absolute numbers. We try our model on six empirical datasets and compare them with null models.

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Acknowledgements

The authors acknowledge financial support by the Swedish Research Council and the WCU program through NRF Korea funded by MEST R31–2008–10029. The authors thank Taro Takaguchi for comments.

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Authors and Affiliations

  1. IceLab, Department of Physics, Umeå University, 90187, Umeå, Sweden

    Fariba Karimi & Petter Holme

  2. Department of Energy Science, Sungkyunkwan University, Suwon, 440–746, Korea

    Petter Holme

  3. Department of Sociology, Stockholm University, 10691, Stockholm, Sweden

    Petter Holme

Authors
  1. Fariba Karimi
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  2. Petter Holme
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Corresponding author

Correspondence to Petter Holme .

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Editors and Affiliations

  1. Ice Lab, Department of Physics, Umeå University, Ice Lab, 3rd floor, NA wing, Naturvetarhuset, Umeå, 901 87, Sweden

    Petter Holme

  2. and Computational Sciences (BECS), Department of Biomedical Engineering, Aalto University, Rakentajanaukio, Otaniemi campus 2, Aalto, 00076, Finland

    Jari Saramäki

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Karimi, F., Holme, P. (2013). A Temporal Network Version of Watts’s Cascade Model. In: Holme, P., Saramäki, J. (eds) Temporal Networks. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36461-7_16

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  • DOI: https://doi.org/10.1007/978-3-642-36461-7_16

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36460-0

  • Online ISBN: 978-3-642-36461-7

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