Fig. 2

Analysis of the changes of the modularity and the robustness by edge-removal mutations in T-LGL signaling network. The removal rate of edges was varied from 1% to 5% (More specifically, the numbers of removed edges were 2, 3, 4, 5, and 7, respectively, among a total of 142 edges). For each removal rate, 5000 trials of edge-removal were examined. See Additional file 1: Fig. S1 and S2 for the analysis results of STF and HIV-1 signaling networks. a Results of average changes of the modularity and the robustness against the removal rate of edges. Y-axis value and error bar represents the average and the standard deviation divided by the square root of the sample size (5000), respectively. Both average values were significantly larger than zero (All P-values <0.0001 using one-sample t-test). The one-sample t-test was valid because the average values were normally distributed (see Additional file 1: Fig. S3) and there were no or very few significant outliers (see Additional file 1: Fig. S6). b-c Relationship between the changes of the modularity and the robustness in the case that the removal rate is 1% and 2%, respectively. A significant negative relationship was observed (Correlation coefficients were −0.33042 and −0.31208 in (b) and (c), respectively, with all P-values <0.0001). This relationship was consistently observed for larger removal rates (see Additional file 1: Fig. S9). d A trend of correlation coefficients between the changes of the modularity and the robustness against the removal rate of edges