Constant State of Change: Engagement Inequality in Temporal Dynamic Networks

TL;DR

This paper introduces two indices to measure engagement inequality in dynamic interaction networks, revealing their stability over time and their ability to distinguish different networks, with notable exceptions like Enron.

Contribution

The study develops novel temporal engagement indices and demonstrates their stability and discriminative power across various real-world networks.

Findings

Indices are stationary for most networks despite fluctuations.

Over 80% of weekly index changes are less than 10%.

A classifier can identify networks based on indices with high accuracy.

Abstract

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.