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Title: Optimizing target nodes selection for the control energy of directed complex networks
Authors: Chen, Hong
Yong, Ee Hou
Keywords: Science::Physics
Issue Date: 2020
Source: Chen, H., & Yong, E. H. (2020). Optimizing target nodes selection for the control energy of directed complex networks. Scientific Reports, 10, 18112-. doi:10.1038/s41598-020-75101-w
Project: 04INS000175C230
Journal: Scientific Reports 
Abstract: The energy needed in controlling a complex network is a problem of practical importance. Recent works have focused on the reduction of control energy either via strategic placement of driver nodes, or by decreasing the cardinality of nodes to be controlled. However, optimizing control energy with respect to target nodes selection has yet been considered. In this work, we propose an iterative method based on Stiefel manifold optimization of selectable target node matrix to reduce control energy. We derive the matrix derivative gradient needed for the search algorithm in a general way, and search for target nodes which result in reduced control energy, assuming that driver nodes placement is fixed. Our findings reveal that the control energy is optimal when the path distances from driver nodes to target nodes are minimized. We corroborate our algorithm with extensive simulations on elementary network topologies, random and scale-free networks, as well as various real networks. The simulation results show that the control energy found using our algorithm outperforms heuristic selection strategies for choosing target nodes by a few orders of magnitude. Our work may be applicable to opinion networks, where one is interested in identifying the optimal group of individuals that the driver nodes can influence.
ISSN: 2045-2322
DOI: 10.1038/s41598-020-75101-w
Schools: School of Physical and Mathematical Sciences 
Rights: © 2020 The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit
Fulltext Permission: open
Fulltext Availability: With Fulltext
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