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I saw this chart on the BBC today:

Before/after

I would like to create a similar chart, but i do not know what the chart is called to learn how to build this in R.

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They are called Sankey Diagrams.

There are a few different options to create these in R. Your example could have been created with straight lines using parallel sets. There are a few other R packages though that can make more complicated diagrams, see this SO Q/A for some examples.

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