Mean-field analysis of the convergence time of message-passing computation of harmonic influence in social networks

Wilbert Samuel Rossi*, Paolo Frasca*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)


The concept of harmonic influence has been recently proposed as a metric for the importance of nodes in a social network. A distributed message passing algorithm for its computation has been proposed by Vassio et al. (2014) and proved to converge on general graphs by Rossi and Frasca (2016a). In this paper, we want to evaluate the convergence time of this algorithm by using a mean-field approach. The mean-field dynamics is first introduced in a “homogeneous” setting, where it is exact, then heuristically extended to a non-homogeneous setting. The rigorous analysis of the mean-field dynamics is complemented by numerical examples and simulations that demonstrate the validity of the approach.

Original languageEnglish
Pages (from-to)2409-2414
Number of pages6
Issue number1
Publication statusPublished - Jul-2017
Externally publishedYes


  • Convergence analysis
  • Distributed algorithm
  • Message passing
  • Nonlinear recursion
  • Opinion dynamics
  • Social networks

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