## 5 Results
### Discriminating Efficiencies by Ranking Centralities  
Many methods of discriminating between DEA results have been proposed [68; 69; 70]. [PERSON] and [PERSON] [60] suggested a method that turns DEA results into a network for the second stage analysis, and uses the tools developed in the social network analysis community to further discriminate DEA results. At this point, and using the results previously presented in this section, we run the mechanism adapted from [PERSON] and [PERSON] [60]. Aggregated lambda values are presented in Appendix B. As follows from our adaptation of [PERSON] and [PERSON]'s model, we create a network based on the lambda values resulting from benchmarking the efficiencies obtained by the DEA analysis with the different proposed models. Then we calculated the eigenvector centrality of different companies in order better to discriminate efficiencies of DMUs. We present the ranking obtained in Table 8. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Estimate**} & \multicolumn{4}{c}{**Incremental Model**} \\ \cline{2-5}  & **Business Step 2** & **Network Step 4** & **Social Media Step 6** & **Overall Step 9** \\ \hline Number efficient DMUs & 22 & 24 & 27 & 30 \\ \% efficient DMUs & 51.16 & 55.81 & 62.79 & _69.77_ \\ Original average efficiency score & 0.7893 & 0.8261 & 0.8738 & 0.9017 \\ Average bias-corrected efficiency score & 0.7714 & 0.8081 & 0.8645 & 0.8949 \\ Bias & 0.0179 & 0.0200 & 0.0093 & 0.0068 \\ Standard deviation & 0.0090 & 0.0090 & 0.0046 & 0.0034 \\ Average efficiency score of inefficient & & & & \\ DMUs corrected & 0.5318 & 0.5657 & 0.6359 & 0.6523 \\ Bootstrap median & 0.7771 & 0.8418 & 0.8690 & 0.8978 \\ Lower bound & 0.7200 & 0.7589 & 0.8279 & 0.8685 \\ Upper bound & 0.7900 & 0.8267 & 0.8740 & 0.9019 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Original and bootstrapped DEA efficiency coefficients of overall steps. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Rank** & **Airline** & **Centrality** & **Rank** & **Airline** & **Centrality** \\ \hline
1 & Air Europa & 1.000 & 23 & Jet2.com & 0.024 \\
2 & Scandinavian Airlines System & 0.811 & 24 & Ryanair & 0.024 \\
3 & Air Berlin & 0.770 & 25 & Aer Lingus & 0.023 \\
4 & Monarch Airlines & 0.690 & 26 & Alttalia & 0.016 \\
5 & Norwegian Air Shuttle & 0.588 & 27 & British Airways & 0.016 \\
6 & Sunexpress & 0.433 & 28 & Icelandair & 0.016 \\
7 & Adria Airways & 0.382 & 29 & Finnair & 0.008 \\
8 & Ukraine International Airlines & 0.362 & 30 & Aeroflot Russian Airlines & 0 \\
9 & Volotea & 0.279 & 31 & Air Baltic & 0 \\
10 & easylet & 0.215 & 32 & Belavia Belarusian Airlines & 0 \\
11 & Aegean Airlines & 0.192 & 33 & Czech Airlines & 0 \\
12 & Lufthansa & 0.182 & 34 & Flybe & 0 \\
13 & Wizz Air & 0.169 & 35 & Iberia Airlines & 0 \\
14 & Vueling Airlines & 0.125 & 36 & KLM Royal Dutch Airlines & 0 \\
15 & Croatia Airlines & 0.100 & 37 & LOT Polish Airlines & 0 \\
16 & Virgin Atlantic Airways & 0.085 & 38 & Luxair & 0 \\
17 & Brussels Airlines & 0.076 & 39 & Meridiana & 0 \\
18 & Bulgaria Air & 0.054 & 40 & TAP Portugal & 0 \\
19 & Air France & 0.046 & 41 & TAROM & 0 \\
20 & S7 Airlines & 0.040 & 42 & Travel Service & 0 \\
21 & Air Malta & 0.032 & 43 & Turkish Airlines & 0 \\
22 & Air Serbia & 0.032 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Ranking of DMUs by their eigenvector centrality. Results show that bigger companies, in terms of incomes or engagement in social media, are not the most efficient ones when sorted after applying the mechanism. This leads us to think whether the management strategy those big companies are following has been correctly designed. More recent companies, compared to the rulers of the market in the last 50 years (Turkish Airlines, KLM, or TAP), such as AirEuropa, Air Berlin, or SAS seem to better perform in the current market. Reasons might be very diverse: from a more specific passenger target to the decision of operating in a more local area or region. Figure 1 represents the weighted network of airlines by using their lambda values.