## 4 Results and Discussion
### Flight Routes Visualization
Figure 14a shows the result of applying this modification and it is clear that _North_ and _South America_ have significantly reduced their size, while _Europe_ and _Asia_ have significantly increased their size. From this, it can be seen that the density of routes relative to the number of airports  
Figure 13: (**a**) Flight dataset’s initial visualization, depicting the hierarchy totally uncollapsed. Adjacency edges represent air routes among airports that are hierarchically structured into cities, regions, countries, and continents. (**b**) Dataset completely collapsed at the continent level. The angle occupied by the sectors is proportional to the number of airports. The black filling of the square placed in each sector is indicative of the connectivity degree. _Asia_ and _Europe_ show a high degree of connectivity in relation to their number of airports. is much higher in _Europe_ and _Asia_, while in the two American continents there are more airports, but some of them operate few passenger routes. Looking at the thicknesses of the meta-connections associated with the continents in Figure 14a, it is easy to see that the number of internal routes in _Europe_, _North America_, and _Asia_ is very high in comparison with the number of external routes with any of the other continents. If we eliminate from the visualization the self-connections (Figure 14b) and focus on the routes between continents, it is clearly perceived that _Europe_ and _Asia_ are the two most highly connected continents, followed by _Europe_ to _North America_, and _Europe_ to _Africa_. With the purpose of inspecting the routes between the two most connected continents (_Europe_ and _Asia_), we proceed to filter out the rest of continents and uncollapse _Europe_ (Figure 15a). To reduce visual clutter, sibling connections at the country level (in this case, European internal routes) can be depicted on the outward side, allowing a better analysis of the available routes between Asia and European countries (Figure 15b). It is immediately observed that _Russia_ is the country of the European continent with the highest number of routes to _Asia_, followed by _United Kingdom_ and _Germany_. Uncollapsing _Asia_ we see that _Turkey_ is the Asian country most connected to _Europe_ (Figure 15c). With the aim of inspecting the connections across European countries, we can focus on the European continent by discarding the rest of the hierarchy from the visualization. Figure 16a, where _Europe_ is shown as the root of the sunburst, reveals that _Spain_ and _Germany_ are the two most highly connected European countries. By disaggregating _Spain_ and highlighting the connections from _Germany_, it can be clearly seen that the regions of _Spain_ with which _Germany_ mainly connects are the _Canary Islands_, the _Balearic Islands_ and _Andalusia_ (Figure 16b). Returning to the highest level of abstraction and visualizing again the meta-connections between continents (Figure 14a), we realize that, while _Europe_ and _Asia_ were the most highly connected, the meta-connection linking _Africa_ and _South America_ appears with a very small thickness, which indicates that there are few routes between the two continents. For further analyzing this fact, we focus on both continents by filtering out the rest of the meta-nodes and disaggregating _South America_ at the country level (Figure 17a). In this view, it is clear that there is only one edge connecting _Africa_ to _Brazil_, which implies that _Brazil_ is the only country in _South America_ that has air routes to the African continent. By uncollapsing _Africa_ we can now analyze which African countries _Brazil_ has routes to. Since we have already identified _Brazil_ as the only South American country with routes to _Africa_, we can perform  
Figure 14: (**a**) The angle occupied by the sectors is now proportional to their connectivity degree. Note that _North America_ and _South America_ have reduced its size considerably, while _Europe_ and _Asia_ have increased it significantly.