For each network, we test if it is near a critical point by computing its heat capacity. A divergence in the heat capacity is a sufficient indicator of a continuous phase transition indicating the presence of a critical point with maximal sensitivity to parametrical changes1. In our model, the heat capacity is represented by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C(\beta )=-\,\beta \frac{\partial H}{\partial \beta }=$$\end{document}C(β)=−β∂H∂β=\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\beta }^{2}(\langle {E}^{2}(s)\rangle -{\langle E(s)\rangle }^{2})$$\end{document}β2(〈E2(s)〉−〈E(s)〉2), where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E(s)=-\,{\sum }_{i}{h}_{i}{s}_{i}-{\sum }_{i < j}\,{J}_{ij}{s}_{i}{s}_{j}$$\end{document}E(s)=−∑ihisi−∑i<jJijsisj is the energy of the Ising model and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H=-\,\sum _{s}P(s)$$\end{document}H=−∑sP(s)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{log}\,(P(s))$$\end{document}log(P(s)) is the entropy of the system. So we test if a system is at criticality by using the entropy H of the system as an order parameter and looking for continuous phase transitions associated with critical points. We detect a continuous phase transition if the entropy presents a sharp but continuous transition in which the derivative of the entropy (the heat capacity) diverges as the system size increases.