## 5 Results
### Discussion on the Results  
We illustrate our approach clearly, using a bubble chart to visualize the information so that the relationship between airline centrality and efficiency can be checked. We try to show how eigenvector centrality values influence the efficiency of airlines taken into account other factors (engagement, fleet size, and income). The following bubble charts combine efficiency (X axis) and the eigenvector centrality calculated as detailed in Section 3.3.2 (Y axis). The size of the bubbles is determined by engagement, (Figure 2), fleet number (Figure 3), and income (Figure 4).  
Figure 1: Airline lambda-based network displayed by eigenvector centrality (darker and bigger nodes represent greater efficiency).  
The graph is divided into four quadrants. The first quadrant is the upper right-hand corner of the graph, where we see airlines with efficiency and eigencentrality values close to 1 (Air Europa, Scandinavian Air Lines, Air Berlin, Monarch Airlines, Norwegian Air)--that is, 10.6% of the sample.  
Figure 4: Bubble chart representing efficiency vs. eigencentrality. Node size denotes airline total incomes.  
Figure 3: Bubble chart representing efficiency vs. eigencentrality. Node size denotes airline fleet volume.  
Figure 2: Bubble chart representing efficiency vs. eigencentrality. Node size denotes engagement for the company in social media.  
The second quadrant, in the lower right-hand corner, includes low values of eigencentrality and a range of efficiency between 0.5 and 1, and corresponds to 72.3% of the European airlines studied. The third quadrant, the lower left-hand corner, includes low values of both x and y (Luxair, Travel Service, Meridiana, TAROM, Turkish Airlines), and that corresponds to 17.2% of the sample. Finally, the fourth quadrant, the upper left-hand corner, includes high values of eigencentrality and low values of efficiency: we can observe that there is not one airline in this quadrant, which is consistent with benchmark's definition. From a quality perspective, we can find three groups of airlines. The first group (first quadrant) corresponds to the group leaders: the majority are efficient and are the most referenced for the rest of the DMU (despite not having a big income and their fleet not being particularly large, nor even their engagement in social media). We might suggest that this type of airline chooses a segmentation market strategy and operates on the optimal scale. In other cases, companies cannot achieve their objectives (growth, profitability, market presence, social recognition, etc.) within their current activity and opt for another type of strategy: diversification. This is the situation of the second group (second quadrant, right side): efficient airlines with low values for eigencentrality (such as Air France or Lufthansa), large fleet, their own way of operating, and singular features.  
In the third group, we find low values of eigencentrality, inefficient airlines, with low-medium income and fleet and with a reasonable value for engagement in social networks. These airlines should leverage their recognition and positioning in social media as an intangible value and improve the way they operate.  
For further details on the results, please check Appendices A and B.