Abstract
Predicting the evolution of viral processes on networks is an important problem with applications arising in biology, the social sciences, and the study of the Internet. In existing works, mean-field analysis based upon degree distribution is used for the prediction of viral spreading across networks of different types. However, it has been shown that degree distribution alone fails to predict the behavior of viruses on some real-world networks and recent attempts have been made to use assortativity to address this shortcoming. In this paper, we show that adding assortativity does not fully explain the variance in the spread of viruses for a number of real-world networks. We propose using the graphlet frequency distribution in combination with assortativity to explain variations in the evolution of viral processes across networks with identical degree distribution. Using a data-driven approach by coupling predictive modeling with viral process simulation on real-world networks, we show that simple regression models based on graphlet frequency distribution can explain over 95% of the variance in virality on networks with the same degree distribution but different network topologies. Our results not only highlight the importance of graphlets but also identify a small collection of graphlets which may have the highest influence over the viral processes on a network.
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Notes
Disconnected graphlets have also been considered in several graphlet-based works, but in this work we only consider connected graphlets because connectedness is essential for the evolution of a viral process on a network.
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This work was supported in part by NSF Grants SCC-1737585, SES-1343123, ATD-1737996, and ATD-1737925.
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Communicated by Mason A. Porter and Andrea L. Bertozzi.
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Khorshidi, S., Al Hasan, M., Mohler, G. et al. The Role of Graphlets in Viral Processes on Networks. J Nonlinear Sci 30, 2309–2324 (2020). https://doi.org/10.1007/s00332-018-9465-y
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DOI: https://doi.org/10.1007/s00332-018-9465-y