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Universality in network dynamics

A Corrigendum to this article was published on 05 November 2013

This article has been updated

Abstract

Despite significant advances in characterizing the structural properties of complex networks, a mathematical framework that uncovers the universal properties of the interplay between the topology and the dynamics of complex systems continues to elude us. Here we develop a self-consistent theory of dynamical perturbations in complex systems, allowing us to systematically separate the contribution of the network topology and dynamics. The formalism covers a broad range of steady-state dynamical processes and offers testable predictions regarding the system’s response to perturbations and the development of correlations. It predicts several distinct universality classes whose characteristics can be derived directly from the continuum equation governing the system’s dynamics and which are validated on several canonical network-based dynamical systems, from biochemical dynamics to epidemic spreading. Finally, we collect experimental data pertaining to social and biological systems, demonstrating that we can accurately uncover their universality class even in the absence of an appropriate continuum theory that governs the system’s dynamics.

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Figure 1: The observed dynamical behaviour of model systems.
Figure 2: Local dynamics: stability and impact.
Figure 3: Propagation of perturbations.
Figure 4: Cascade sizes.
Figure 5: Uncovering the dynamical universality class from empirical data.

Change history

  • 09 October 2013

    In the version of this Article originally published, the expression for Gij on page 673 should have included an absolute value sign. In addition, the caption for Fig. 1b1–c4 was missing the final wording: (note that the bounded distributions here and throughout are normalized to have mean zero and variance one). These errors have been corrected in the HTML and PDF versions of the Article.

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Acknowledgements

We thank A. Vespignani, A. Sharma, F. Simini, J. Menche, S. Rabello, G. Ghoshal, Y-Y Liu, T. Jia, M. Pósfai, C. Song, Y-Y. Ahn, N. Blumm, D. Wang, Z. Qu, M. Schich, D. Ghiassian, S. Gil, P. Hövel, J. Gao, M. Kitsak, M. Martino, R. Sinatra, G. Tsekenis, L. Chi, B. Gabriel, Q. Jin and Y. Li for discussions, and S. S. Aleva, S. Weiss, J. de Nicolo and A. Pawling for their support. This work was supported by DARPA Grant Number 11645021; The DARPA Social Media in Strategic Communications project under agreement number W911NF-12-C-0028; the Network Science Collaborative Technology Alliance sponsored by the US Army Research Laboratory under Agreement Number W911NF-09-02-0053; the Office of Naval Research under Agreement Number N000141010968 and the Defense Threat Reduction Agency awards WMD BRBAA07-J-2-0035 and BRBAA08-Per4-C-2-0033; the National Institute of Health, Center of Excellence of Genomic Science (CEGS), Grant number NIH CEGS 1P50HG4233; and the National Institute of Health, Award number 1U01HL108630-01.

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Both authors designed and performed the research. B.B. carried out the analytical and numerical calculations and analysed the empirical data. A-L.B. was the lead writer of the manuscript.

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Correspondence to Albert-László Barabási.

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Barzel, B., Barabási, AL. Universality in network dynamics. Nature Phys 9, 673–681 (2013). https://doi.org/10.1038/nphys2741

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