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Time-dependent influence metric for cascade dynamics on networks.

James P Gleeson1, Ailbhe Cassidy1, Daniel Giles2

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Summary
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A new algorithm efficiently calculates expected cascade size on networks. This method identifies influential nodes early or late in the spreading process, generalizing previous centrality measures for network dynamics.

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Area of Science:

  • Network Science
  • Computational Social Science
  • Epidemiology Modeling

Background:

  • Understanding information or disease spread on networks is crucial.
  • Identifying influential nodes is key for targeted interventions.
  • Existing centrality measures may not capture time-dependent influence.

Purpose of the Study:

  • To propose and test an efficient algorithm for calculating expected cascade size.
  • To enable the identification of influential nodes based on their timing in the spreading process.
  • To generalize existing methods for influential node identification in network dynamics.

Main Methods:

  • Development of a novel algorithm for expected cascade size calculation.
  • Testing the algorithm's accuracy across different dynamic regimes (critical and subcritical).
  • Comparison with nonbacktracking centrality for identifying influential single spreaders.

Main Results:

  • The proposed algorithm efficiently calculates time-dependent expected cascade size.
  • The measure accurately identifies influential nodes, distinguishing early and late spreaders.
  • The method generalizes nonbacktracking centrality, proving effective in critical and subcritical dynamics.

Conclusions:

  • The developed algorithm provides an accurate and efficient tool for analyzing network cascade dynamics.
  • It enhances the ability to identify key influencers in spreading processes over time.
  • This work offers a generalized approach to centrality measures for network influence.