The authors consider Sankey diagrams as directed weighted graphs but they “can be difficult, time-consuming, and uninteresting to render by hand”. However, “Sankey diagrams do add an indisputable expressive power to a standard mathematical rendering of a graph…[and] when professionally constructed, Sankey diagrams represent flow in a manner … can be understood by anyone, instantly.”

Three diagrams are presented: a simple directed, weighted graph representing a candy factory, a pen-sketched B/W Sankey diagram, and the corresponding Sankey diagram in SVG format, created using data in XML format and XSLT style sheet transformation.

They also have some interesting details on graphical problems, such as overlay, edge layout, width of Sankey arrows in curves, etc. Basically all that stuff that developers of professional Sankey software tools have to cope with.