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Controlling edge dynamics in complex networks

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Abstract

The interaction of distinct units in physical, social, biological and technological systems naturally gives rise to complex network structures. Networks have constantly been in the focus of research for the past decade, with considerable advances in the description of their structural and dynamical properties. However, much less effort has been devoted to studying the controllability of the dynamics taking place on them. Here we introduce and evaluate a dynamical process defined on the edges of a network, and demonstrate that the controllability properties of this process significantly differ from simple nodal dynamics. Evaluation of real-world networks indicates that most of them are more controllable than their randomized counterparts. We also find that transcriptional regulatory networks are particularly easy to control. Analytic calculations show that networks with scale-free degree distributions have better controllability properties than uncorrelated networks, and positively correlated in- and out-degrees enhance the controllability of the proposed dynamics.

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Figure 1: SBD on a simple network and its mapping to the line graph.
Figure 2: Expected fraction of driver nodes nD in various model networks.
Figure 3: The dependence of the fraction of driver nodes nD on the one-point degree correlation ρ.

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Acknowledgements

This research was supported by the European Union, European Research Council COLLMOT project and the European Social Fund No: TAMOP 4.2.1/B-09/1/KMR-2010-0003. We are grateful to E. Mones for useful discussions.

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Authors and Affiliations

Authors

Contributions

T.N. devised the SBD model and performed analytical calculations and simulations.T.V. initiated the research and supervised the project. T.N. and T.V. wrote the paper.

Corresponding author

Correspondence to Tamás Vicsek.

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The authors declare no competing financial interests.

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Nepusz, T., Vicsek, T. Controlling edge dynamics in complex networks. Nature Phys 8, 568–573 (2012). https://doi.org/10.1038/nphys2327

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