## 4 Results  
For each task, global and local efficiency were estimated for each hemisphere at time T0 and T1. Figures 3-5 show the boxplots of the global efficiency and local efficiency values. A statistical analysis was performed to assess if the differences between the injured (left) and the non-injured (right) hemisphere at T0 and T1 were significant. For this aim, we chose to perform a nonparametric test since the Shapiro-Wilk test [25] revealed that the global and local efficiency values are in some cases normally distributed and in others not normally distributed. In particular, the Wilcoxon rank-sum test [26] was carried out under the null hypothesis that for each task, the medians of the global and local efficiency values between the left and right hemisphere at time T0 do not differ from the corresponding ones at time T1. The significance level was set at 5% so that the difference between T0 and T1 is statistically significant when the \(p\)-value is less than 0.05. Table 1 shows the \(p\)-values derived from the statistical analysis for each task. At T0, for both naming and repetition task, global and local efficiency in the left (impaired) hemisphere are lower than those of the right (unimpaired) hemisphere. For the reading task, conversely, global and local efficiency of the left hemisphere are higher than those of the right hemisphere. All the differences are statistically significant, except for local efficiency related to the naming task. After the rehabilitative treatment, at T1, the global and local efficiency values between the two hemispheres become balanced, and there is no longer a statistically significant difference. This trend reflects the expected behavior, as the rehabilitation contributed to the creation of new neural patterns to compensate for the disrupted ones. The results also suggest that local and global networks of the brain are altered in stroke patients but not always in the same direction. This trend can be due to the effects of stroke, which affect not only the site of structural damage but also distant brain regions that belong to a functional network. The patient also underwent the Aachener Aphasie Test (AAT), a standardized test that provides an assessment of language functioning after brain injury and determines the presence of aphasia [27]. The scores of the AAT at time T0 and T1 show an improvement of the aphasic deficits of the patient (Figure 6). In particular, the batteries of the naming, repetition and written language tests revealed a gain of 17, 9 and 11 points, respectively, after the rehabilitative treatment. Note that the \"written language\" battery includes the tests related to the reading ability assessment. The AAT results support our findings of the functional connectivity analysis. Figure 4: _Cont_. Figure 3: Naming task: boxplot of global efficiency for each hemisphere at time (**a**) T0 and (**b**) T1; boxplot of local efficiency for each hemisphere at time (**c**) T0 and (**d**) T1. On each box, the bottom and the top edges denote the 25 th and 75 th percentiles, respectively; the line inside the box indicates the median; the “whiskers” extend below and above the box up to the minimum and maximum data values, respectively. The ’+’ marker symbol outside the whiskers represents the outliers. Figure 4: Repetition task: boxplot of global efficiency for each hemisphere at time (**a**) T0 and (**b**) T1; boxplot of local efficiency for each hemisphere at time (**c**) T0 and (**d**) T1. On each box, the bottom and the top edges denote the 25 th and 75 th percentiles, respectively; the line inside the box indicates the median; the “whiskers” extend below and above the box up to the minimum and maximum data values, respectively. The ‘+’ marker symbol outside the whiskers represents the outliers. Figure 5: Reading task: boxplot of global efficiency for each hemisphere at time (**a**) T0 and (**b**) T1; boxplot of local efficiency for each hemisphere at time (**c**) T0 and (**d**) T1.