networks thresholded at Dmin; 2) comparing the AUC of the regional network measures over the specified density range; 3) performing FDA on the regional network curves over the specified density range. GAT outputs both uncorrected and false discovery rate (FDR) corrected p-values as measures of significance of the regional measures comparisons. GAT also generates the plots of between-group differences in regional network measures along with the quantified confidence intervals as a function of network density. Network hub analysis. Hubs are crucial components for efficient communication in a network. Hubs are not only considered as important regulators of information flow but also play a key role in network resilience to insult [27]. Previous studies demonstrated that the hubs in the human brain structural correlation networks tend to be the regions in highly connected association cortex [13] and that the distribution of hubs are altered in structural networks of patients with Schizophrenia, Alzheimer’s disease and multiple sclerosis [12,14,15]. A node is considered as a hub if its regional degree/betweenness centrality is 1 (or 2) SD higher than the mean network degree/betweenness [12,20]. GAT quantifies the network hubs based on measures of degree, betweenness centrality, local efficiency or local clustering and a user-defined SD cutoff. The same as for regional measures, three approaches are taken for quantification of hubs. 1) The hubs are quantified for networks thresholded at Dmin; 2) the hubs are quantified based on the AUC of the degree (or betweenness, etc.) in the specified density range; 3) the hubs are quantified from FDA of the degree (or betweenness, etc.) curves in the specified density range. Random failure and targeted attack analysis. To assess the resilience of brain networks to acute and focal damage, networks can be lesioned by random deletion of nodes, or by targeted attack on the highest-degree nodes in the network [56]. In GAT, random failure of the networks is simulated by randomly removing one node from the network and then measuring changes in global network metrics (e.g. size, path length, etc.) of the remaining largest component. This process is repeated by incrementally removing additional nodes randomly until the size of the largest component is 1 [3,57]. To assess the network behavior against targeted attack, the same procedure is applied. However, in this case, the nodes are removed in rank order of decreasing nodal measure (e.g. nodal betweenness, degree, etc.). Several global metrics like size, path length, mean local and global efficiency as well as a number of nodal metrics like nodal degree and betweenness have been suggested in the literature for assessing random failure and targeted attack analysis [3,11,14,20,58]. In GAT, user may pick among several regional (e.g. degree, betweenness, clustering) and global metrics (e.g. size, mean local and global efficiency, path length) to investigate the effect of random failure and targeted attack on network behavior. The user can specify the density threshold at which random failure and targeted attack analysis are performed. To test whether two group networks behave differently against random failure and targeted attack, a permutation analysis (same as the procedure mentioned for analyzing between-group differ- ences in network measures) is performed. Then, the difference in network behavior is measured either at each attack (failure), through FDA or AUC analysis. Network modularity analysis. Modularity is a more sophisticated measure of network segregation and is quantified by subdividing the network into groups of regions that have maximal within group connections and minimal between-group links. A unique advantage of modular organization is that it can evolve one module at a time, without risking loss of function in GAT: Graph Analysis Toolbox for Brain Networks other modules [59]. Optimization algorithms are usually used to find such modular structures within a network. GAT uses the algorithms described in [60] and [61], and implemented in BCT, for quantification of modular structure. In order to characterize the degeneracy of the modularity structure adequately, the optimization algorithm runs several times (the number of iterations (default is 100) is specified by the user). Then, the community structure with highest maximized modularity value is used as the representative modular structure. Network visualization. For visualization of networks on brain templates, GAT takes two approaches: first, GAT directly maps the network structure on an axial view of anatomical brain template (T1 image). Each ROI is represented by one node whose world coordinate has been extracted from AAL atlas. The brain networks are then mapped using these nodal dimensions. Second, GAT creates the node and edge files required by BrainNet Viewer (http://www.nitrc.org/projects/bnv/) in order to visualize the connectivity patterns. This way, you can use the files generated by GAT in BrainNet Viewer and visualize the networks and hub structures. Degree distribution. Pattern of distribution of nodal con- nectivity in a network (degree distribution) reveals specific characteristics of the network and its resilience to random failure and targeted attacks [3,13,62]. Previous studies have demonstrated that the degree distribution of small-world structural brain networks follows an exponentially truncated power-law distribu- tion [13,63]. Such distribution is formulated as P(d) , [d(e21) * exp(-d/dc)], where P(d) is the probability of network regional degree (d), dc is the cut-off degree above which there is an exponential decay in probability of hubs and e is the exponent, and indicates a scaling regimen, followed by an exponential decay in the probability of nodes with nodal degree greater than a cutoff value of dc; suggesting a network which mostly comprised of nodes with a nodal degree close to average network degree and also a number of nodes with higher number of connections (hubs). GAT examines whether the cumulative degree distribution of the constructed networks follows an exponentially truncated power- law distribution and returns the R-square, which is a measure of how successful the fit is (R-square value close to 1 represents a perfect fit). It also generates a figure showing the original and fitted degree distributions. The cumulative degree distribution is used to reduce the effects of noise on smaller data sets [64]. There are also other forms of degree distribution observed in real-world networks including power law degree distribution (d2e) and exponential degree distribution (e2e*d). GAT also compares the R-square values for exponentially truncated power law fit model, power law fit model and exponential fit model. Functional Graphs Based on Resting-state or Task-based fMRI Data Temporal correlations in spontaneous low-frequency fluctua- tions in blood oxygen level dependent (BOLD) signal while subjects rest has been demonstrated as a reliable measure of brain connectivity [65–67]. The small-worldness of resting-state func- tional networks have been consistently demonstrated in several fMRI studies [3,5,16,68,69]. In addition, resting state fMRI connectivity studies are sensitive to abnormal global network organization, revealing changes in several clinical populations with cognitive deficits including Alzheimer’s disease [5,9], schizophre- nia [70,71], traumatic brain injury [72], temporal lobe epilepsy [73], depression [10,26] and attention-deficit hyperactivity disor- der [74]. On the other hand, task-based functional connectivity pattern, i.e. temporal correlations of low-frequency BOLD signal while a subject performs a task, has also been shown to reflect the PLoS ONE | www.plosone.org 5 July 2012 | Volume 7 | Issue 7 | e40709