Figure 4

The Role of Edges. (a) The proportion of critical \(m_\mathrm{C}\), ordinary \(m_\mathrm{O}\), and intermittent \(m_{\mathrm{I}}\) edges in each real network with the coupling density \(P=0\), \(P=0.2\), \(P=0.4\), and \(P=1\), respectively. The proportion (b) \(M_\mathrm{C}^\mathrm{analytic}\), (c) \(M_\mathrm{O}^\mathrm{analytic}\), and (d) \(M_{\mathrm{I}}^\mathrm{analytic}\) obtained by theoretical prediction, compared with the real results. The variation of \(m_\mathrm{C}\), \(m_\mathrm{O}\), and \(m_{\mathrm{I}}\) in (e–g) ER networks, (h–j) EX networks, and (k–m) SF networks as the function of the coupling density P, the average degree \(\langle k \rangle \) and the power exponent \(\gamma \), respectively.