Structure and dynamical behavior of non-normal networks

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We analyze a collection of empirical networks in a wide spectrum of disciplines and show that strong non-normality is ubiquitous in network science. Dynamical processes evolving on non-normal networks exhibit a peculiar behavior, as initial small disturbances may undergo a transient phase and be strongly amplified in linearly stable systems. In addition, eigenvalues may become extremely sensible to noise and have a diminished physical meaning. We identify structural properties of networks that are associated with non-normality and propose simple models to generate networks with a tunable level of non-normality. We also show the potential use of a variety of metrics capturing different aspects of non-normality and propose their potential use in the context of the stability of complex ecosystems.
Original languageEnglish
Article numbereaau9403
Pages (from-to)eaau9403
JournalScience Advances
Issue number12
Publication statusPublished - 12 Dec 2018


  • non normal network
  • complex network
  • non normal dynamic
  • networked systems
  • network models
  • empirical networks
  • Lotka-Volterra model


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