Fig. 4: Comparing the robustness of the real biological multilayer networks (filled symbols) and randomized models (unfilled symbols).
From: Robustness and lethality in multilayer biological molecular networks
The results are averaged over 30 realizations. Higher values mean greater robustness of the system. The real model has comparable robustness as a the model that is disassortatively randomized in the gene regulatory network, and higher robustness than b the model that is assortatively randomized in the gene regulatory network. Here, the result in the metabolic layer is evaluated by setting the threshold fP2M = 0.7, and the results under other threshold values are shown in (c), where \({R}_{{\rm{Meta}}}^{{\rm{O}}}\) and \({R}_{{\rm{Meta}}}^{{\rm{CRN-Rand}}}\), respectively, represent the integral size of the functional metabolic network in the real and randomized models, with p varying from 0 to 1. If the value \({R}_{{\rm{Meta}}}^{{\rm{O}}}-{R}_{{\rm{Meta}}}^{{\rm{CRN-Rand}}}\) is larger than zero under different thresholds, the real model is more robust than the assortatively randomized model (GRN-Assort). The real metabolic layer has comparable robustness with the disassortatively randomized model (GRN-DisAssort), since \({R}_{{\rm{Meta}}}^{{\rm{O}}}-{R}_{{\rm{Meta}}}^{{\rm{CRN-Rand}}}\) is near zero under different thresholds; d the real model is also more robust than the randomized model in which the gene–protein connections are assortatively rewired.
