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Structure and dynamical behavior of non-normal networks | Science Advances
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.

Also here
https://arxiv.org/abs/1801.07351
networks  linear_algebra  dynamical_system  network_data_analysis  teaching  ? 
10 weeks ago by rvenkat
Essence of linear algebra - YouTube
Видеокурс по линейной алгебре
video  courses  math  linear_algebra 
december 2018 by gevorg

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