Quantum transport senses community structure in networks

TL;DR

This paper introduces a quantum transport-based clustering algorithm that effectively detects complex community structures in networks, demonstrating robustness and comparable performance to spectral clustering.

Contribution

The authors develop a novel quantum transport clustering method using Laplace transforms to map networks onto a circle, enhancing community detection in complex networks.

Findings

QTC matches spectral clustering in pattern recognition

QTC is more robust with density variations

QTC effectively detects complex network communities

Abstract

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 an 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 as powerful as the state-of-the-art spectral clustering in discerning complex geometric patterns and more robust when clusters show strong density variations or heterogeneity in size. 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. Python source code implementing the algorithm and examples are available at https://github.com/jssong-lab/QTC.