Structure and dynamical behavior of non-normal networks

Malbor Asllani; Renaud Lambiotte; Timoteo Carletti

doi:10.1126/sciadv.aau9403

Structure and dynamical behavior of non-normal networks

Malbor Asllani, Renaud Lambiotte, Timoteo Carletti

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Abstract

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 language	English
Article number	eaau9403
Pages (from-to)	eaau9403
Journal	Science Advances
Volume	4
Issue number	12
DOIs	https://doi.org/10.1126/sciadv.aau9403
Publication status	Published - 12 Dec 2018

Keywords

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

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10.1126/sciadv.aau9403Licence: CC BY-NC

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http://advances.sciencemag.org/content/4/12/eaau9403

Cite this

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title = "Structure and dynamical behavior of non-normal networks",

abstract = "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.",

keywords = "non normal network, complex network, non normal dynamic, networked systems, network models, empirical networks, Lotka-Volterra model",

author = "Malbor Asllani and Renaud Lambiotte and Timoteo Carletti",

note = "Funding Information: Gratitude goes to D. Fanelli and P. K. Maini for useful discussions. The work of M.A. and T.C. presents research results of the Belgian Network DYSCO, funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office. The work of M.A. was also supported by an FRS-FNRS Postdoctoral Fellowship. Author contributions: M.A. and T.C. designed the study, conducted the formal analysis, and analyzed the data. All authors organized and wrote the manuscript. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors. Publisher Copyright: Copyright {\textcopyright} 2018 The Authors, some rights reserved. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.",

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doi = "10.1126/sciadv.aau9403",

language = "English",

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AU - Lambiotte, Renaud

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PY - 2018/12/12

Y1 - 2018/12/12

N2 - 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.

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Structure and dynamical behavior of non-normal networks

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Structure and dynamical behavior of non-normal networks

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Keywords

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Reaction-diffusion equations: the role of geometry and granularity

Competitive and diffusive processes in complex networks and time-delayed systems

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High Performance Computing Technology Platform

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SIAM Conference Dynamical Systems

complenet19

Séminaire Résidentiel 2019

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