## 4 Experimental Results
### Feature Importance  
In the second part of our analysis, we evaluated which features had a special role in the disease prediction. To this end, we used the feature ranking methods described in Section 3.4. It is worth to note that, for a more robust evaluation, we computed the importance rankings over a hundred of different random sub-samples of the subjects having the same class distribution of the original sample. We found 25 region pairs in common to the 90 th percentile of the importance distribution of the three methods. The region pairs with the highest relative importance, in accordance with the AAL2 atlas, are depicted in Figure 3. Instead, Table 2 shows the seven regions which occurred more than one time in the 25 most important region pairs. Finally, Table 3 shows the anatomical areas whose regions  
Figure 2: Classification performance. in the discrimination between pathological and controls and explore the most relevant AD-related brain regions at the whole brain level. In doing this, we extended our previous research [15; 16] by addressing two major open issues. As first important issue, since in [15] the goal was to compare communicability to other traditional network metrics, we used only one classification algorithm. In this work, we employed three different state-of-the-art classification algorithms in order to evaluate if the information content of communicability is robust against the use of a particular learning algorithm. We found that all the models employed, i.e., SVMs, RFs and ANNs, provided comparable values of accuracy, AUC and specificity, which are in line with our previous work. Instead, for what concerns sensitivity, a significantly higher value was obtained with ANN and thus we can conclude that this classification model is more sensitive to detect the disease starting from the features used in this analysis. There is usually a trade-off between sensitivity and specificity. A sensitivity higher than specificity is preferable in diagnosis support systems, as this means that the system is better in detecting the presence of disease in the pathological group rather than detecting the absence of disease in the healthy group. Therefore, the system is more effective for ruling out disease when resulting in a negative response. In addition, it is worth to remark that the high value of sensitivity has been here obtained with a perfectly balanced dataset. Having balanced data provides more reliable evaluation of the performance, as it is well known that, in case of unbalanced data, classification algorithms tend to favor the correct prediction of the over-represented class instead of the other ones. However, it is worth noting that in a clinical context achieving a high sensitivity is of paramount importance, so it could be appropriate to explore also situations with unbalanced datasets or adopt strategies that alleviate the risk of overlooking the diagnosis [40]. The second important issue concerns the dependence of the proposed method on the network size. In our previous work [15], coarse anatomical connectivities were considered for the estimated brain networks. Connectivities obtained between relatively large region patterns are more robust and reproducible; however, they could overlook detailed patterns of connectivity, which may play a key role in neurological diseases investigation.This issue was partially addressed in [16], where we focused only on the subcortical sub-network. In this paper, we further extended our previous studies by taking into account a different parcellation scheme and a different reconstruction of the brain connectivity network to study patterns of connectivity emerging at the whole-brain level. First of all, we observed that the most significant brain region pairs involve connections between cortical regions or between subcortical regions and cortical regions.