Sankey Diagram. Energy flow charts of the US and China

This post is a part of my notes on linear algebra.

A Sankey diagram is a visual display of the flow of a scalar.  In a Sankey diagram, the width of each branch of the flow is proportional to the magnitude of the scalar.

Flow of a scalar.  Water flows from mountains to oceans.  Commodities flow from producers to consumers.  Money changes hands.  Electric charge flows in circuits.  The flow of a scalar can often be complex, from many sources, via many branches, to many sinks.

An excellent way to visualize the flow of a scalar is to plot a Sankey diagram, in which the width of each branch of the flow is proportional to the magnitude of the scalar, and different branches are additive. Thus, a Sankey diagram visualizes the flow by taking advantage of the scalar properties:  additivity, scalability, and proportionality.

Energy flow chart. Every year the Lawrence Livermore National Laboratory publishes a Sankey diagram of the flow of energy in the United States.  The diagram is called the energy flow chart.

I wrote a google doc to explain the Sankey diagram to sudents in my undergraduate class on linear algebra. I also attach a pdf file below.