  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.
