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The global public sphere has changed dramatically over the past decades: a significant part of public discourse now takes place on algorithmically driven platforms owned by a handful of private companies. Despite its growing importance, there is scan t large-scale academic research on the long-term evolution of user behaviour on these platforms, because the data are often proprietary to the platforms. Here, we evaluate the individual behaviour of 600,000 Twitter users between 2012 and 2019 and find empirical evidence for an acceleration of the way Twitter is used on an individual level. This manifests itself in the fact that cohorts of Twitter users behave differently depending on when they joined the platform. Behaviour within a cohort is relatively consistent over time and characterised by strong internal interactions, but over time behaviour from cohort to cohort shifts towards increased activity. Specifically, we measure this in terms of more tweets per user over time, denser interactions with others via retweets, and shorter content horizons, expressed as an individuals decaying autocorrelation of topics over time. Our observations are explained by a growing proportion of active users who not only tweet more actively but also elicit more retweets. These behaviours suggest a collective contribution to an increased flow of information through each cohorts news feed -- an increase that potentially depletes available collective attention over time. Our findings complement recent, empirical work on social acceleration, which has been largely agnostic about individual user activity.
Spatially embedded networks have attracted increasing attention in the last decade. In this context, new types of network characteristics have been introduced which explicitly take spatial information into account. Among others, edge directionality p roperties have recently gained particular interest. In this work, we investigate the applicability of mean edge direction, anisotropy and local mean angle as geometric characteristics in complex spherical networks. By studying these measures, both analytically and numerically, we demonstrate the existence of a systematic bias in spatial networks where individual nodes represent different shares on a spherical surface, and describe a strategy for correcting for this effect. Moreover, we illustrate the application of the mentioned edge directionality properties to different examples of real-world spatial networks in spherical geometry (with or without the geometric correction depending on each specific case), including functional climate networks, transportation and trade networks. In climate networks, our approach highlights relevant patterns like large-scale circulation cells, the El Ni~{n}o--Southern Oscillation and the Atlantic Ni~{n}o. In an air transportation network, we are able to characterize distinct air transportation zones, while we confirm the important role of the European Union for the global economy by identifying convergent edge directionality patterns in the world trade network.
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