## 4 Results and Discussion
### Flight Routes Visualization  
In this example, we will show how Carbonic can be used for the exploration of flight routes at different levels of abstraction. The dataset used for that purpose combines two datasets: _OurAirports_ ([[https://ourairports.com/data/](https://ourairports.com/data/)]([https://ourairports.com/data/](https://ourairports.com/data/)) accesssed on 10 June 2022), and _OpenFlights_ ([[https://openflights.org/data.html](https://openflights.org/data.html)]([https://openflights.org/data.html](https://openflights.org/data.html)), accesssed on 10 June 2022). The _OurAirports_ dataset stores the airports and will allow the creation of the hierarchical structure based on the location of the airport: city, region, country, and continent. On the other hand, the _OpenFlights_ database provides the air routes between the airports spanning the globe. In this way, the leaf nodes are the airports and the edges indicate that there is a route between the two incident airports. Additionally, the dataset has been filtered to  
Figure 12: Highlighting or summarizing hidden information. (**a**) The image shows the result of mapping the angle of each sector to its connectivity degree. Those sectors whose angular size turns out to be below a threshold are enclosed in an orange circle, meaning that there is not enough screen space available to render them in detail. (**b**) Relevant features of the hidden tree under each collapsed node are summarized by a simple glyph. In this example, the width of the black filling encodes the number of leaf nodes, while the height of the black filling represents the depth of the hidden tree. discard inconsistencies, leaving a total of 19,222 connections among 55,741 airports. The _OurAirports_ dataset also provides other attributes for the airports which can be used in Carbonic for filtering operations. In this example we have used the attribute \"Type\" which can have the following values: _large airport_, _medium airport_, _small airport_, _sealplane base_, or _heliport_. Figure 13a shows the initial Carbonic visualization of the complete dataset, where the colors of the sectors follow the tree color palette, the size of the leaf nodes is unitary, and the nodes have been alphabetically sorted. The high complexity of the scene does not allow to discern the nodes from each other and it becomes impossible to follow the trajectory of the connections, presenting the usual hairball effect. Rolling up to the highest level of abstraction makes it possible to obtain a global view of the whole data without the need to look at each airport and each connection individually. This can be seen in Figure 13b where a global collapsing has been performed, visualizing only the meta-nodes of the highest level of abstraction, which in this case corresponds to the continents. Since the size assigned to the leaf nodes is unitary, we see that the continents occupying a larger angle are those with a larger number of airports (in the example, _North America_ followed by _Europe_ and _South America_). Looking at the square marks placed in each sector, we observe that the continent with a higher connectivity degree is _North America_, followed by _Asia_ and _Europe_. It seems coherent that the continent with the largest number of airports is, at the same time, the one with the most air routes. However, it is striking that _Asia_ has such a high degree of connectivity, occupying such a small angle. This imbalance encourages us to further explore the distribution of connections and airports. By applying a property-based filter, we can remove closed airports, heliports, and seaplane bases from the visualization. This will allow us to remove elements that are not relevant, in this case, airports that do not have commercial routes. If we now map the degree of connectivity to the angle of the leaf nodes, then the largest continents will be those having the most routes.