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| Comparative Study of Spectral Properties Between Complex Networks and Quantum Dynamical Systems |
| YE Bina, XU Shuaia, WANG Xue-songa, QIU Liangb
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| a. School of Information and Electrical Engineering; b. College of Science, China University of Mining and Technology, Xuzhu 221116, China |
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Abstract By mapping the adjacency matrix of a complex network to Hamiltonian of a quantum system, the statistical properties of the spectra and eigenstates are analyzed. The spectral statistics, i.e. the nearest-neighbor spacing distribution, the number variance and the spectral form factor, are analyzed numerically. The results show that when the rewiring probability of small-world network model is lower, the spectral properties are consistent with those of quantum integrable systems. When the rewiring probability is higher than a certain threshold, its energy spectrum properties are similar to those of the Gaussian orthogonal ensembles in random matrix theory. These results hint that certain analogies may exist between the spatial topology of complex networks and the temporal evolution properties of quantum dynamical systems.
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Received: 25 April 2013
Published: 22 June 2026
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