There are places where the embedding of the graph will have edges that have discrete meaning. For example, distances, or if the graph is being drawn on say a grid. Lines and curves are easy to understand to represent as a the edges, it is simple. read more
A graph of a set of data is represented by lines or curves and not discrete points because the data is continuous. This means that the data is measured and that there are possible values in between the measured values. Data that are counted, on the other hand, are discrete data and the graph would be drawn as discrete points. read more