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Connectomes with high sensitivity and high specificity are unattainable with current axonal fiber reconstruction methods, particularly at the macro-scale afforded by magnetic resonance imaging. Tensor-guided deterministic tractography yields sparse connectomes that are incomplete and contain false negatives (FNs), whereas probabilistic methods steered by crossing-fiber models yield dense connectomes, often with low specificity due to false positives (FPs). Densely reconstructed probabilistic connectomes are typically thresholded to improve specificity at the cost of a reduction in sensitivity. What is the optimal tradeoff between connectome sensitivity and specificity? We show empirically and theoretically that specificity is paramount. Our evaluations of the impact of FPs and FNs on empirical connectomes indicate that specificity is at least twice as important as sensitivity when estimating key properties of brain …