Quantum transport senses community structure in networks
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Quantum time evolution exhibits rich physics, attributable to the interplay between the density and phase of a wave function. However, unlike classical heat diffusion, the wave nature of quantum mechanics has not yet been extensively explored in modern data analysis. We propose that the Laplace transform of quantum transport (QT) can be used to construct a powerful ensemble of maps from a given complex network to a circle S^1, such that closely-related nodes on the network are grouped into sharply concentrated clusters on S^1. The resulting QT clustering (QTC) algorithm is shown to outperform the state-of-the-art spectral clustering method on synthetic and real data sets containing complex geometric patterns. The observed phenomenon of QTC can be interpreted as a collective behavior of the microscopic nodes that evolve as macroscopic cluster orbitals in an effective tight-binding model recapitulating the network.
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