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?
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
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.