Potential energy of complex networks: a quantum mechanical perspective.

ABSTRACT: We propose a characterization of complex networks, based on the potential of an associated Schrödinger equation. The potential is designed so that the energy spectrum of the Schrödinger equation coincides with the graph spectrum of the normalized Laplacian. Crucial information is retained in the reconstructed potential, which provides a compact representation of the properties of the network structure. The median potential over several random network realizations, which we call ensemble potential, is fitted via a Landau-like function, and its length scale is found to diverge as the critical connection probability is approached from above. The ruggedness of the ensemble potential profile is quantified by using the Higuchi fractal dimension, which displays a maximum at the critical connectio

SUBMITTER: Amoroso N 

PROVIDER: S-EPMC7592062 | biostudies-literature | 2020 Oct

REPOSITORIES: biostudies-literature