Detecting Structure of Complex Network by Quantum Bosonic Dynamics

TL;DR

This paper introduces a quantum bosonic model to analyze complex network structures, revealing properties like connected components and random walk dynamics, with results aligning with traditional graph theory.

Contribution

The paper presents a novel quantum bosonic approach to uncover topological features of complex networks, providing analytical insights and numerical validation.

Findings

Ground state degeneracy equals number of connected components.

Square of ground state coefficients relates to random walk times.

First excited state appears on the largest connected component.

Abstract

We introduce a non-interacting boson model to investigate topological structure of complex networks in the present paper. By exactly solving this model, we show that it provides a powerful analytical tool in uncovering the important properties of real-world networks. We find that the ground state degeneracy of this model is equal to the number of connected components in the network and the square of coefficients in the expansion of ground state gives the averaged time for a random walker spending at each node in the infinite time limit. Furthermore, the first excited state appears always on its largest connected component. To show usefulness of this approach in practice, we carry on also numerical simulations on some concrete complex networks. Our results are completely consistent with the previous conclusions derived by graph theory methods.