world index in the ALL network at several densities across the range (p,0.05) (Fig. 6). FDA and AUC analysis on global network measures. In addition to comparing networks at various densities, we compared the AUC for global network measure curves (density range of 0.22:0.01:0.45) between groups. Similar to the observed differ- ences across densities, while the ALL network had non- significantly smaller AUC for normalized clustering (p = 0.079) and larger normalized path length (p = 0.352), it showed a significantly smaller small-worldness (p = 0.043) compared with CON network. The FDA results were also consistent with the AUC results; ALL network had non-significantly smaller normal- ized clustering (p = 0.080), larger normalized path length (p = 0.352), and significantly smaller small-world index (p = 0.041). Between-group Differences in Regional Network Measures Differences at Dmin. [Thightest]We investigated between- group differences in regional network measures, specifically nodal betweenness, on networks thresholded at Dmin. Regions including left middle frontal gyrus, left medial superior frontal and right supramarginal gyrus showed significantly smaller betweenness in ALL network. Conversely, a number of regions including right insula, right inferior parietal and left supramarginal gyrus showed significant larger betweenness in ALL network. None of these regions survived after correction for multiple comparisons (P,0.05). FDA and AUC analysis on regional network measures. We also compared the AUC for regional network measure curves (density range of 0.22:0.01:0.45) between groups (Fig. 7). While some of the regions were common between AUC analysis and analysis of network differences at Dmin a number of different regions were also found. Specifically, left orbital inferior frontal, and right triangular inferior frontal regions showed significantly smaller betweenness in ALL while left insula showed significantly larger betweenness in ALL. None of these regions survived after correcting for multiple comparisons (p,0.05) so the regional results are considered exploratory. The FDA results were similar to AUC results. Network Hubs We considered a node as a hub if its regional betweenness centrality is 2 SD higher than the mean network betweenness. Hubs were quantified for networks thresholded at Dmin as well as based on FDA and the AUC of nodal betweenness curves (density range of 0.22:0.01:0.45). For networks thresholded at Dmin, the ALL network hubs were found in the right inferior parietal lobule, left supramarginal gyrus, left postcentral gyrus and right rolandic operculum whereas the CON network hubs were found in the right cuneus, left middle frontal gyrus, left medial superior frontal gyrus, bilateral postcentral gyrus, and right supramarginal gyrus. Hub quantification based on AUC analysis revealed ALL network hubs in the right insula, right inferior parietal, right rolandic operculum and left supramarginal gyrus and CON network hubs in the left middle frontal gyrus, left medial superior frontal gryus, right inferior parietal lobule and bilateral postcentral gyrus (Fig. 8). Hubs quantified using FDA were exactly the same as those obtained from AUC analysis. Random Failure and Targeted Attack Analysis In order to analyze the networks behavior in response to random failure, we calculated the size of the largest remaining component in response to successive removal of nodes, in random order. Changes in size of the remained largest component of the GAT: Graph Analysis Toolbox for Brain Networks network as a function of fraction of randomly removed nodes are depicted in Fig. 9A. In most of the fractions of removed nodes, the resilience of the ALL network to random failure was significantly reduced compared to CON (p,0.05). The AUC of the curve was also significantly lower in the ALL network compared to CON (p = 0.043). The FDA results were also consistent with the AUC results showing significantly lower robustness to random failure in the ALL network (p = 0.042). The same procedure was applied to analyze the networks behavior in response to targeted attack but removing the nodes in rank order of decreasing nodal betweenness centrality. The CON network was generally more robust to targeted attack compared to ALL network and the difference reached significance at a few fractions of attacked nodes (p,0.05) (Fig. 9B). The AUC for the CON network was larger than for the ALL but it was not significant (p = 0.175). The same results were observed using FDA. Network Modularity Analysis Global network modularity was significantly higher in the CON network compared with the ALL across several network densities (Fig. 10A). The FDA and AUC analysis also revealed a significantly higher modularity in the CON network in the density range of interest (0.22:0.01:0.45) (p = 0.023 for AUC analysis and p = 0.024 for FDA). Five modules were found in the networks of both groups as color-coded in Figure 10B. Degree Distribution The degree distribution in both networks followed an exponen- tially truncated power-law distribution (P(d) , [d(e21) * exp(2d/ dc)]) (Fig. 11). The exponent estimate (e) was 1.19 for ALL and 1.27 for CON networks. The cut-off degree (dc) was 2.65 for ALL network and 2.52 for the CON. The R-square value was 0.97 for both groups’ distributions fits. We also compared the goodness-of- fit for other forms of degree distribution. The R-square for BC group was 0.56 for power law fit and 0.91 for exponential fit. For the CON group, the R-square value was 0.50 for power law fit and 0.85 for exponential fit. Discussion Graph theoretical analyses of neuroimaging data have increased our understanding of the organization of structural and functional brain networks in recent years. In this report, we describe the development of a graph analysis toolbox (GAT) that facilitates analysis and comparison of structural and functional brain networks. We demonstrated the capabilities of GAT by investi- gating the differences in organization of structural brain networks in survivors of acute lymphoblastic leukemia (ALL) and healthy matched Controls (CON). The results revealed an alteration in small-world characteristics of the brain structural networks in the ALL network; an observation that confirms our hypothesis suggesting widespread neurobiological injury in ALL survivors. This is the first report of altered large-scale structural brain networks in ALL survivors. Large-scale Structural Networks in ALL Global network measures. Both the ALL and CON networks followed a small-world organization across a wide range of densities (Fig. 5). Such a network allows for efficient information processing by providing an optimal balance between segregation and integration [14]. The results are in line with previous graph analysis studies that have consistently shown a small-world architecture in structural brain networks in healthy individuals [12,19,47]. PLoS ONE | www.plosone.org 10 July 2012 | Volume 7 | Issue 7 | e40709