Constant state of change: engagement inequality in temporal dynamic networks

Hadar Miller, Osnat Mokryn

Research output: Contribution to journalArticlepeer-review


The temporal changes in complex systems of interactions have excited the research community in recent years as they encompass understandings on their dynamics and evolution. From the collective dynamics of organizations and online communities to the spreading of information and fake news, to name a few, temporal dynamics are fundamental in the understanding of complex systems. In this work, we quantify the level of engagement in dynamic complex systems of interactions, modeled as networks. We focus on interaction networks for which the dynamics of the interactions are coupled with that of the topology, such as online messaging, forums, and emails. We define two indices to capture the temporal level of engagement: the Temporal Network (edge) Intensity index, and the Temporal Dominance Inequality index. Our surprising results are that these measures are stationary for most measured networks, regardless of vast fluctuations in the size of the networks in time. Moreover, more than 80% of weekly changes in the indices values are bounded by less than 10%. The indices are stable between the temporal evolution of a network but are different between networks, and a classifier can determine the network the temporal indices belong to with high success. We find an exception in the Enron management email exchange during the year before its disintegration, in which both indices show high volatility throughout the inspected period.

Original languageEnglish
Article number84
Pages (from-to)1-14
JournalApplied Network Science
Issue number1
StatePublished - 1 Dec 2019

Bibliographical note

Funding Information:
This research was supported by the ISRAEL SCIENCE FOUNDATION (grant No. 82371/).

Funding Information:
This work was partially supported by the Israel Science Foundation Grant #328/17.

Publisher Copyright:
© 2019, The Author(s).


  • Dominance
  • Engagement indices
  • Gini-index inequality
  • Interactions intensity

ASJC Scopus subject areas

  • General
  • Computer Networks and Communications
  • Computational Mathematics


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