Figure 4
From: Potential energy of complex networks: a quantum mechanical perspective
Left panel: complex network with \(N=500\) nodes, generated using the ER model with connection probability \(p=p_c=1/(N-1)\simeq 2\cdot 10^{-3}\) (graph generated with the Python libraries Graphviz 2.3837 and NetworkX 2.438). Central panel: shifted graph spectrum \(E_n\) (red horizontal lines) and reconstructed potential V(x) (green, only positive x displayed) corresponding to the network in the left panel, with x the dimensionless variable of the Schrödinger equation (4). Right panel: ensemble potential \(V_m(x)\) over \(M=100\) network realizations with the same N and p.
