# Governance and Dynamic Efficiency with Network Structure in the Brazilian Natural Gas Utilities
## 3 Results  
The divisions are considered vectors, whose weight indicates their importance in the process of pipeline gas companies. However, the literature does not provide a degree of importance that highlights one division over the other. Therefore, in this study, we used an equal weight of 0.5 for each division. To maintain the evaluation over a 6-year period, equal weights were assigned both to the period and to the divisions. Thus, in this study, we assume that all processes have the same importance, corroborating the same assumption made by [33, 79, 80]. By applying the DNSBM model, an overall efficiency score was generated for each distribution company, covering the efficiency results of the two divisions for the entire period, as well as obtaining an overall efficiency score per period, considering the results of each year individually. Similarly to the overall efficiency analysis, efficiency scores were calculated for the technical-operational division (DIV TO) and the economic-financial division (DIV EF). For the analysis of the overall and divisional efficiency scores, it is important to clarify that they range from 0 to 1. Those DMUs that obtain a score of 1 are considered efficient, thus forming the efficiency frontier. This leads us to interpret that the closer to 0, the worse the performance of the DMU in terms of relative efficiency. According to [PERSON] [32], the greater the distance from the frontier, the more effort will be needed by the DMUs to improve input processes and product generation. Thus, Table 3 presents a summary of the efficiency results. It is observed that the overall efficiency has an average score of 0.7496, with a standard deviation of 0.3032. These results indicate an intermediate level of efficiency in the segment, suggesting that pipeline gas distributors have been seeking improvements in their activities, which in turn have directly impacted technical-operational as well as economic-financial improvements, averaging 25%. The year 2015 is noted as the period of highest efficiency (0.8300), with the DIV TO and DIV EF scores being 0.7788 and 0.8518, respectively. When analyzing the segregation of the distributors' scores, it was observed that in the lower quartile, 29% of the companies have a performance considered weak in the segment. From the 1 st quartile to the median, characterized as a reasonable performance, at least 24% of the distributors are included. In the analysis of the overall efficiency scores (\(\uptheta_{0}^{*}\)) the behavior of each distributor within the studied period, as well as the ranking through the efficiency score, can be observed in Table 4.  
For the analysis of divisional efficiency (\(\uptheta_{0}^{*}\)) which is explained and discussed in relation to overall efficiency (\(\uptheta_{0}^{*}\)), the DIV TO and DIV EF indicate the performance of efficiency in the production and consumption stages, respectively. DIV EF showed better performance, with an average score of 0.8203 compared to DIV TO, which had an average score of 0.7221. This performance of the divisions means that the products generated in the economic-financial division can be explained by the segment's own evolution, with the growing number of customers, as well as the expansion of the served regions, leading to an increase in gas consumption and financial return. Regarding the number of efficient distributors, there was also variation between the divisions; however, during the study period, as can be observed in Figure 1, DIV TO had a higher number of efficient distributors. Considering the overall efficiency score for all the periods, 11 distributors reached the efficiency frontier in DIV TO and 10 distributors in DIV EF.