For creating and reading data visualizations, visual literacy is crucial. This article advances the knowledge about graphical variations and conventions related to the basic graphical element of the graphical line used as a connector in data visualizations. Some visual characteristics of connecting lines can be used to show directionality and thus signal a narrative claim. Arrowheads may be one way to do so. However, particularly in a digital environment, other techniques may be used as well. This article presents a corpus study investigating the ways in which narrativity is signalled by connecting lines in current, publicly available digital data visualizations. The central connecting lines of 163 award-winning data visualizations are analysed with focus on their visual forms and how they represent actions and situations. The repeated occurrence of some visual techniques points to conventions formed both by a long tradition of analogue visualization and the advent of digital production techniques and output devices. The presented results are relevant to researchers, educators and practitioners in the data visualization field, as they provide novel empirical data on the use of an omnipresent graphical element.