Null-eigenvalue localization of quantum walks on complex networks

@article{Bueno2020NulleigenvalueLO,
  title={Null-eigenvalue localization of quantum walks on complex networks},
  author={Ruben Bueno and Naomichi Hatano},
  journal={arXiv: Physics and Society},
  year={2020}
}
First we report that the adjacency matrices of real-world complex networks systematically have null eigenspaces with much higher dimensions than that of random networks. These null eigenvalues are caused by duplication mechanisms leading to structures with local symmetries which should be more present in complex organizations. The associated eigenvectors of these states are strongly localized. We then evaluate these microstructures in the context of quantum mechanics, demonstrating the… 
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