I got sick of working on my dissertation the other day so I started writing a review article on visualizing flow lines for journey to crime data. Here I will briefly illustrate why great circle lines tend to look nicer in flow maps than do straight lines.
Flow maps tend to be very visually complicated, and so what happens (to a large extent) is what happens in Panel B in the above graphic. Bending the lines, as is done with great circles, tends to displace the lines from one another to a greater extent. Although perfect overlap as is demonstrated in the picture doesn’t necessarily happen that frequently, the same logic applies to nearly overlapped lines. One of the nicest examples of this you can find is the facebook friends map that made the internet rounds (note there are many other aesthetic elements in the plot that make it look nice besides just the great circle lines).
Of course with great circle lines you don’t get the bending in the other direction for reciprocal flows I demonstrate in my first figure (the great circle line is the same regardless of direction). Because of this, and because when using a local projection great circles lines don’t really provide enough eccentricity in the bend to produce the desired displacement of the lines, I suggested to utilize half circles and discuss how to calculate them given a set of origin-destination coordinates at this question on the GIS site.
I need to test this out in the wild some more though. I suspect a half-circle is too much, but my attempts to script a version where the eccentricity is less pronounced has befuddled me so far. I will post an update on here if I come to a better solution, and when the working paper is finished I will post a copy of that as well. Preferably I would like the script to take an arbitrary parameter to control the amount of bend in the arc, so if you have suggestions feel free to shoot me an email or leave a comment here.
For those interested in the topic I would suggest to peruse one of my other answers at the GIS site. Therein I give a host of references and online mapping examples of visualizing flows.