## 5 Experiments
### Simulation Results  
The first set of experiments investigated how accurately egocentric betweenness scores correlated with the sociocentric betweenness scores in a VANET scenario; in other words, how accurate the results were when using only the local knowledge of the network topology to compute the betweenness score in highly dynamic networks, instead of using global knowledge of the topology. The results of this approach are shown in the scatter diagram set in Figure 7, which compares the two approaches for each vehicle traffic density. A scatter plot revealed the relationships between two variables (in our case, such variables were the sociocentric and the egocentric score). The relationship between two variables is known as correlation. The higher the correlation between the two variables, the closer the sample observations will be to a straight line. If the sample observations go along a straight line (or regression line) from the origin to high x- and y-values, then the variables are assumed to have a positive correlation. Thus, it is possible to observe in Figure 7 that the egocentric and the sociocentric betweenness scores have a positive correlation. Figure 7a-e show the scatterplots for densities of 40, 60, 80, 100 and 150 vehicles/km\({}^{2}\), respectively. As can be seen in these figures, these two measures do not provide the same betweenness scores, as expected. The egocentric betweenness scores (y-axis) were smaller than the sociocentric betweenness scores (x-axis). This can be explained by the fact that in the ego-network topology, the maximal geodesic distance between nodes was two, and this limitation did not apply to the sociocentric betweenness. On the other hand, through the analysis of the figures, the egocentric and the sociocentric betweenness scores have demonstrated a high degree of similarity regarding the ranking of nodes. This similarity can be confirmed in Table 4. The table depicts the Pearson correlation coefficient (PCC) between the egocentric and the sociocentric betweenness approaches. The presented values ranged from 0.953-0.983 (where 1.0 represents a perfect linear relationship between the two datasets analysed), in all traffic densities. Lastly, it is possible to notice that some scores lie relatively away from the regression line (red line). Even so, there is a clear positive relationship between the two betweenness measures in VANETs. Figures 8 and 9 depict the cumulative distribution function (CDF), in each vehicle traffic density, of the egocentric betweenness scores and the number of one-hop neighbours, respectively. The CDF measure is an interesting way of observing the behaviour of analysed variables. As can be observed in Figure 8, the egocentric betweenness scores fluctuate in the same range as in Figure 7, according to the vehicle traffic density. Another important information is to analyse the distribution of these scores. It is possible to observe that 90% of the samples, for densities of 40, 60, 80, 100 and 150 vehicles/km\({}^{2}\), were lower than 7, 11, 16, 18 and 30, respectively. In other words, these scores were close to the regression line (red line of Figure 7), i.e., 90% of the samples of the two variables had a high correlation. The same distribution analysis was performed for the number of one-hop neighbours, as shown in Figure 9. In this example, it is possible to notice that 90% of the samples, for densities of 40, 60, 80, 100 and 150 vehicles/km\({}^{2}\), were lower than 7, 9, 12, 14 and 21 neighbours, respectively. Figure 7: Scatterplot of sociocentric vs. egocentric betweenness for each vehicle traffic density. \begin{table}
\begin{tabular}{l c} \hline \hline
**Density (vehicles/km2)** & **PCC** \\ \hline
40 & 0.983 \\
60 & 0.962 \\
80 & 0.971 \\
100 & 0.964 \\
150 & 0.953 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Pearson correlation coefficient (PCC) of egocentric and sociocentric betweenness. Figure 8: CDF of the egocentric betweenness scores in relation to the vehicle traffic densities.