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Diffusion MRI imaging and tractography algorithms have enabled the mapping of the macro-scale connectome of the entire brain. At the functional level, probably the simplest way to study the dynamics of macro-scale brain activity is to compute the "activation cascade" that follows the artificial stimulation of a source region. Such cascades can be computed using the Linear Threshold model on a weighted graph representation of the connectome. The question we focus on is: if we are given such activation cascades for two groups, say A and B (e.g. Controls versus a mental disorder), what is the smallest set of brain connectivity (graph edge weight) changes that are sufficient to explain the observed differences in the activation cascades between the two groups? We have developed and computationally validated an efficient algorithm, TRACED, to solve the previous problem. We argue that this approach to compare the connectomes of two groups, based on activation cascades, is more insightful than simply identifying "static" network differences (such as edges with large weight or centrality differences). We have also applied the proposed method in the comparison between a Major Depressive Disorder (MDD) group versus healthy controls and briefly report the resulting set of connections that cause most of the observed cascade differences.