comparison is meaningful needs to be identified, i.e. the density range in which the networks are not fragmented. Therefore, the individual networks are tested for fragmentation to find the range of densities in which all the nodes are connected at least to one other node. After examining all the networks, the minimum network density at which no individual network is fragmented is identified. The maximum network density is indicated by the user by examining the small-worldness of the individual networks. All the further analyses are performed on the networks thresholded over this density range. In order to test the statistical significance of the between-group differences in network topology and regional network measures, GAT performs a parametric t-test (e.g. 2-sample t-test for comparing two groups) as well as a non-parametric permutation test with 2000 (user defined) repetitions [70]. For permutation testing, in each repetition, the network measures (or residuals) of each individual are randomly reassigned to one of the two groups so that each randomized group had the same number of subjects as the original groups. Then, the differences in network measures between randomized groups (at each network density) are then calculated resulting in a permutation distribution of difference under the hypothesis. The actual between-group difference in network measures is then placed in the corresponding permutation distribution and a two-tailed p-value is calculated based on its percentile position. This results in a p-value of difference at each network density. In addition to comparing global network measures at every density, FDA and AUC analyses are performed to make the between-group comparison less sensitive to the thresholding process. The FDA and AUC analyses are performed for each network measure at the specified density range. To test the significance of the between-group differences, either a nonpara- metric permutation test or a parametric t-test is performed. The same procedure is used to compare the between-group differences in regional network measures. However, for the regional measures, comparison at every network density will result in a large number of comparisons (number of densities 6 number of ROIs). Therefore, the comparison is made on the AUC of regional network measures over the specified density range or on the FDA results. GAT outputs both uncorrected and false discovery rate (FDR) corrected p-values as measures of signifi- cance of regional measures comparisons. In the present study, the p-values reported for regional differences between groups are FDR corrected for multiple comparisons (90 comparisons). Network hub analysis. The same as for structural networks, network hubs for functional networks are quantified based on measures of degree, betweenness, local efficiency or local clustering and a user-defined SD cutoff. For functional networks, the AUC of the nodal measures over the specified density range or the FDA results are used for hub analysis. Alternatively, a user- specified density can be used for hub analysis. Other procedures such as visualization and analysis of degree distribution are similar to the one described for structural networks. Results To demonstrate the capabilities of GAT, we examined the differences in organization of structural brain networks in survivors of ALL, the most common child cancer, and healthy matched controls (CON). The detailed procedures of participants, data acquisition and preprocessing is published elsewhere [34]. In summary, 28 children and adolescents with a history of ALL (age 5.0–19.8 years old) who had completed all anti-cancer treatments GAT: Graph Analysis Toolbox for Brain Networks for at least 6 months as well as 31 healthy controls (age 4.1–18.4 years old), matched for age, gender, maternal education level and minority status, were recruited. The study was approved by the Stanford University Institutional Review Board and the Stanford Cancer Center’s Scientific Review Board and written informed consent was obtained from adult participants or from the parent/ legal guardian of minor participants and assent was obtained from participants age 8 years and older per Stanford University’s regulations. High resolution, 3D spoiled gradient recall MR images were obtained using a 3 Tesla GE Signa whole body scanner (GE Medical Systems, Milwaukee, WI) with the following parameters: repetition time = 6.436 ms, echo time = 2.064 ms, flip angle = 15u, number of excitation = 3, matrix size = 2566256 voxels, field of view = 220, slice thickness = 1.5 mm, 124 contiguous slices. To extract individual gray matter volumes, voxel-based morphometry analysis was conducted in Statistical Parametric Mapping (SPM8) [77] using the VBM8 toolbox (http://dbm.neuro.uni-jena.de/ vbm). We utilized the optimized VBM process [78] which included 1) segmentation and extraction of the brain in native space, 2) normalization of the images to a standard space using a customized pediatric template, created via Template-O-Matic software [79] using images from all subjects, 3) segmentation and extraction of the normalized brain (extraction is repeated to ensure that no non-brain tissues remain), 4) modulation of the normalized images to correct for tissue volume differences due to the normalization procedure, and 5) inspection of the resulting gray matter images by expert raters, blinded to group assignment for quality, guided by boxplots and covariance matrices output by the VBM8 toolbox. The extracted gray matter volume maps were used as the input to GAT for construction and analysis of structural correlation networks. Network Construction Regional gray matter volumes of 90 cortical and subcortical ROIs were extracted by applying AAL parcellation scheme to the individual normalized gray matter images. The extracted regional gray matter volume data were corrected for between group differences in age, gender, total brain volume, and their interactions. For each group, a 90690 association matrix was generated by performing Pearson correlation coefficient between regional gray matter volumes across subjects. Previous studies used Pearson correlation analysis to infer statistical associations in morphometry data between brain regions [13,15,17–20,22]. An alternative measure is partial correlation that attempts to remove the effect of indirect paths [80]. However, partial correlation is not suitable for studies with sample size smaller than the number of ROIs [53]. Binary adjacency matrices were then derived by thresholding the association matrices at a range of densities (Dmin: 0.01:0.45; Dmin = 0.22). The lower bound of the range is determined as the minimum density in which the networks of both groups are not fragmented (Dmin = 0.22). For densities above 0.45 the graphs becomes increasingly random (small-world index ,1.5). Additionally, for anatomical networks, connections above this density are less likely biological [81]. Each of the derived binary adjacency matrices represents a network with a specific density. The resultant association and binary adjacency matrices (thresholded at Dmin) are shown in Fig. 4. Consistent with previous studies [12–14,17,20], the association matrices in both groups exhibited similar patterns of connectivity, with generally strong correlations between bilater- ally homologous regions as well as between regions within the same lobe. PLoS ONE | www.plosone.org 7 July 2012 | Volume 7 | Issue 7 | e40709