Approximating the Controllability Robustness of Directed Random-graph Networks Against Random Edge-removal Attacks

Yang LOU, Lin WANG, Shengli XIE, Guanrong CHEN*

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

4 Citations (Scopus)


Network controllability robustness reflects how well a networked system can maintain its controllability against destructive attacks. Its performance can be measured by a sequence of values that record the remaining controllability of the network after a sequential node-removal or edge-removal attacks. In this paper, a hybrid approximation (HyA) method is proposed to estimate the controllability robustness performance of large-scale directed random-graph (RG) networks under random edge-removal attacks. HyA sufficiently utilizes the similarity between the generation mechanism of the RG networks and the destructing process of random edge-removal attacks. Two threshold values are set to classify general RG networks as ‘dense’, ‘sparse’, or ‘median’, according to the average degree of each network. A two-phase approximation is applied to ‘sparse’ RG networks, while different three-phase approximations are applied to ‘dense’ and ‘median’ RG networks, respectively. Simulation results verify that 1) HyA is able to precisely approximate the controllability curves of RG networks under random edge-removal attacks; 2) HyA is time-efficient as compared to the conventional time-consuming attack simulations.
Original languageEnglish
Pages (from-to)376-388
Number of pages13
JournalInternational Journal of Control, Automation and Systems
Issue number2
Early online date30 Jan 2023
Publication statusPublished - 1 Feb 2023

Bibliographical note

Funding Information:
This research was supported in part by the National Natural Science Foundation of China (No. 62002249, 61873167), in part by the Foundation of Key Laboratory of System Control and Information Processing, Ministry of Education, P. R. China (No. Scip202103), in part by the Lam Woo Research Fund at Lingnan University (No. LWP20012), and in part by the Hong Kong Research Grants Council under the GRF Grant CityU11206320.

Publisher Copyright:
© 2023, ICROS, KIEE and Springer.


  • Complex network
  • controllability
  • directed random graph
  • random edge attack
  • robustness


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