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In some cases, it may be impossible to draw Euler diagrams with overlapping circles to represent all the overlapping subsets in the correct proportions. This type of data then requires using polygons or other figures to represent each set. When dealing with data that describes overlapping subsets, how can I figure out whether a simple Euler diagram is possible?

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    $\begingroup$ I am not familiar with this topic, but I spent in the past a lot of time studying graphs. I think that the property that an Euler diagram could be drawn is related with the planarity of the graph where the sets are the nodes. This paper seems to shade some light on this relation: Ensuring the Drawability of Extended Euler Diagrams for up to 8 Sets. $\endgroup$
    – rapaio
    Jun 13, 2014 at 6:04
  • $\begingroup$ This is a good question. The answer has been laid out in papers relating to various graphing libraries, but it will always depend on the assumptions and restrictions that you put in place. Are the circles area appropriate? Will they always have at least X points of intersection? Are you limited in size or quantity of categories? More importantly is the question of whether or not a Euler diagram will be useful. More than a dozen intersecting circles is hard to interpret, but if there's a mostly hierarchical relationship that you are depicting a much larger quantity can work. $\endgroup$ Jun 13, 2014 at 9:48
  • $\begingroup$ I could be wrong and there's an easier test, but with my experience with visualizations, the question has always been a practical one first, and honestly if I'm looking at intersecting categories I usually have a small collection of them. $\endgroup$ Jun 13, 2014 at 9:53
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    $\begingroup$ I'm assuming that by "simple" you mean the diagram uses only circles and that by "proportional" you mean that the area of each section of the diagram is proportional to the population it represents from the total set. It might help to make these definitions explicit in the question. $\endgroup$
    – Air
    Jun 18, 2014 at 23:04

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If you are interested in an empirical solution, you might consider the Venneuler package in R. It provides residuals (percentage difference between input intersection area and fitted intersection area).

https://www.rforge.net/doc/packages/venneuler/venneuler.html

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