Benchmarking Measures of Network Controllability on Canonical Graph Models
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Benchmarking Measures of Network Controllability on Canonical Graph Models Elena Wu-Yan1,2 · Richard F. Betzel2 · Evelyn Tang2 · Shi Gu2 · Fabio Pasqualetti3 · Danielle S. Bassett2,4,5,6 Received: 21 September 2017 / Accepted: 5 February 2018 © The Author(s) 2018. This article is an open access publication
Abstract The control of networked dynamical systems opens the possibility for new discoveries and therapies in systems biology and neuroscience. Recent theoretical advances provide candidate mechanisms by which a system can be driven from one pre-specified state to another, and computational approaches provide tools to test those mechanisms in real-world systems. Despite already having been applied to study network systems in biology and neuroscience, the practical performance of these tools and associated measures on simple networks with pre-specified structure has yet to be assessed. Here, we study the behavior of four control metrics (global, average, modal, and boundary controllability) on eight canonical graphs (including Erd˝os–Rényi, regular, small-world, random geometric, Barábasi–Albert preferential attachment, and several modular networks) with different edge weighting schemes
Communicated by Paul Newton. Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00332018-9448-z) contains supplementary material, which is available to authorized users.
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Danielle S. Bassett [email protected]
1
Department of Computer and Information Sciences, University of Pennsylvania, Philadelphia, PA 19104, USA
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Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104, USA
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Department of Mechanical Engineering, University of California, Riverside, CA, USA
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Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA
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Department of Neurology, Hospital of the University of Pennsylvania, Philadelphia, PA 19104, USA
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Department of Physics & Astronomy, University of Pennsylvania, Philadelphia, PA 19104, USA
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J Nonlinear Sci
(Gaussian, power-law, and two nonparametric distributions from brain networks, as examples of real-world systems). We observe that differences in global controllability across graph models are more salient when edge weight distributions are heavy-tailed as opposed to normal. In contrast, differences in average, modal, and boundary controllability across graph models (as well as across nodes in the graph) are more salient when edge weight distributions are less heavy-tailed. Across graph models and edge weighting schemes, average and modal controllability are negatively correlated with one another across nodes; yet, across graph instances, the relation between average and modal controllability can be positive, negative, or nonsignificant. Collectively, these findings demonstrate that controllability statistics (and their relations) differ across graphs with different topologies and that these differences can be muted or accentuated by differences in the edge weight distribu
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