Why R is not significant (and very low), while all predictors are significant? I used a network logistic regression to regress five predictors against a dependent. They are all significant, instead the R is not significant and it's even very low. I can understand that it may be low because I need to add predictors but I cannot explain why it's not significant. Do you have any idea about?
 A: Short answer: please check what R^2 value you are reporting. Many LR implementations report pseudo R^2 values such as McFadden or adjusted McFadden for which values in the range 0.2-0.4 indicate good model fit. See this guide on psuedo R and this SO answer
Update:
The individual coefficients can be significant due to the occurrence of significant interactions between your independent variables. For instance, whilst bid price may have an insignificant association to same_cartel alone, the combination of bid price and other variable may generate some significant association to your target same_cartel variable. 
It may be useful to assess the collinaearity of your predictors using spearman rank correlation or OLS regression (on any continuous variables) and chi-square (on any categorical variables). Alternatively or in addition, try running your logistic regression with each predictor individually. You could also try step wise pruning if your input variables - though this is not best practice. 
If you discover some collinearity between your predictors it is possible to generate a new features by combining the associated variables into a new “interaction term”. This page provides a nice summary of interaction terms.
Also, the model p-values you obtain will depend upon your sample size. If you have a small sample it is more appropriate to comment on the effect and significance of each predictor variable rather than the model as a whole.
