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To estimate gene regulatory networks, it is important that we know the number of connections, or sparseness of the networks. It can be expected that the robustness to perturbations is one of the factors determining the sparseness. We reconstruct a semi-quantitative model of gene networks from gene expression data in embryonic development and detect the optimal sparseness against perturbations. The dense networks are robust to connectionremoval perturbation, whereas the sparse networks aredoi:10.1371/journal.pone.0176492 pmid:28430819 pmcid:PMC5400252 fatcat:wysrauabzbc35ftriik77lctca