Leaping off from the point of "visualizing the networks between countries and continents imposed by visa status", one can imagine multitudes of visualizations: force-layout, Sankey-diagram, sunburst, etc. One that jumped out as a possibly interesting approach was a hive-plot.
One immediate advantage to the hive plot, is the way that it naturally handles grouping, but shows all of the edges and spreads them out. In our case, we do have a natural clustering on nodes(the countries) given by continents. Next, one observes that there are four statuses that a visa between two countries can take: free, on-arrival, required, refused. One can imagine that free means that no visa is required, on-arrival means that no prior arrangements are needed, required means that one must arrange ahead of time, and refused is, well, a special designation when a passport is not permitted entry to a country or territory. One might immediately guess that a hive plot with seven "arms" corresponding to seven continents(we seprate Central America into its own, but exclude Antarctica), and colored edges to represent the four statuses. However, let's take a minute to compute:
222^2=49284
that's a LOT of edges. Additionally, because countries share continents, there are edges between nodes on a single axis as well(this would take the form of another visualization called a Chord Diagram). For the purpose of producing a beautiful picture, this might be appropriate, for the purpose of a meaningful data visualization, this falls seriously short. So next one might attempt to reduce the dataset to something more manageable, and this is where the hard work comes in.
A first attempt at reducing the data set would be a similar visualization to before, but only showing one status at a time. Given that refused status is rare for most countries, one could think of this producing four visualizations, three of which are rougly 50k/3~16k and one of considerably smaller size. Unfortunately, 16k is still quite too large, and in fact the free and on-arrival graphs actually take the lion's share. Additionally, we still have the issue of edges between countries on the same continent.
Reducing the dataset to something managable requires us to change the structure of our visualization a bit. Stepping away from the assumption that "arms" should correspond to individual continents, we can actually find a better way: by considering arms for each status, and only considering two continents at a time.
This means that there will be 7^2=49 visualizations(one for each pair, allowing for a pair of the same continent). We designate one of the pair's elements to be the source continent, and the other to be the destination. Now we fan the destination continent's countries over the four axes based on the status of the visa to that country. The primary axis at zero degrees represents the source or "origin". We still color based on status for readability, and to create a clear correlation between amount of a color on the graph, and the frequency of that status in the continent pair. Note that we only draw nodes that have at least one edge incedent on them. In the case where a country has no relationships(edges) of a particular visa-status, that country will not appear as a node on that axis of the visualization.
Note that the need for self-edges in the form of a chord diagram on one axis is removed by the ability to select the same continent for the source and target.
Often these projects are presented as "here is the final beautiful version because we're so smart". In the spirit of communicating the real path taken in this visualization, here are some things that didn't work:
One might think "all the countries in Scandanavia probably have the same visa policies"; one would be wrong. You could ask this for countries in the Carribean, Central America, Pacific Islands, or whatever else you dream up.
In fact, no two countries in any continent share exactly the same visa policies, not even when reducing to free, on-arrival, or required statuses
We implemented a method to compair every pair of countries in a continent to find candidates for this kind of reduction, and were shocked at how distict the visa policies are.
One might guess that groups of countries would create a kind of sub-network of 'free' visas. While this is true to a certain extent, it doesn't fit with our general data model, and doesn't show information about all countries. It is, however, interesting as a supplement.
An early mistake was showing all nodes from a continent on each status-axis. Initially our idea was that this would give a sense of the proportion of countries on a continent that have that status from the source continent. However, the huge amount of isolated nodes on the graph was extremely ugly. In some network visualization examples, isolated nodes are important, and tell you extremely important information about the network, but not in our case. The information provided by these isolated nodes, was uninteresting for the most part, and can be inferred without them being there. Also, a small factor was that reducing the number of target nodes by 3/4 improves visualization performance.
We chose primary colors because the number of necessary colors was small. We scaled the axes based on the number of nodes corresponding to that target/continent combination.
First, the user needs to be able to select the continent pair, so two drop downs select source and target continents. Additionally, there is actually more information than the four options of visa status. In reality, the visa status also has information about term and additional notes. The term field is how long the visa actually lasts for. The notes information is additional requirements, cautions, and useful reminders that might be less common, and are important for any travelers to that country. These appear on mouseover, as to allow the graph to remain approachable, but reveal the full richness of the data. Also on mouseover, a stroke is applied to the node an all incident edges. This is to allow for a summary of the local network of that node given by visas.
An additional feature would be to add an accompanying pie chart along side the hive plot so that one could see the shares of the world population "open" to a traveler starting from one country, with the various statuses.