Towards Optimal Robustness of Network Controllability: An Empirical Necessary Condition

Yang LOU, Lin WANG, Kim Fung TSANG, Guanrong CHEN*

*Corresponding author for this work

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

6 Citations (Scopus)


To better understand the correlation between network topological features and the robustness of network controllability in a general setting, this paper suggests a practical approach to searching for optimal network topologies with given numbers of nodes and edges. Since theoretical analysis seems impossible at least in the present time, exhaustive search based on optimization techniques is employed, firstly for a group of small-sized networks that are realistically workable, where exhaustive means 1) all possible network structures with the given numbers of nodes and edges are computed and compared, and 2) all possible node-removal sequences are considered. A main contribution of this paper is the observation of an empirical necessary condition (ENC) from the results of exhaustive search, which shrinks the search space to quickly find an optimal solution. ENC shows that the maximum and minimum in- and out-degrees of an optimal network structure should be almost identical, or within a very narrow range, i.e., the network should be extremely homogeneous. Edge rectification towards the satisfaction of the ENC is then designed and evaluated. Simulation results on large-sized synthetic and real-world networks verify the effectiveness of both the observed ENC and the edge rectification scheme. As more operations of edge rectification are performed, the network is getting closer to exactly satisfying the ENC, and consequently the robustness of the network controllability is enhanced towards optimum.

Original languageEnglish
Pages (from-to)3163-3174
Number of pages12
JournalIEEE Transactions on Circuits and Systems I: Regular Papers
Issue number9
Early online date24 Apr 2020
Publication statusPublished - Sep 2020
Externally publishedYes

Bibliographical note

Funding Information:
This work was supported in part by the Hong Kong ITF under Grant CityU ITP/058/17LP, in part by the National Natural Science Foundation of China under Grant 61873167, and in part by the Natural Science Foundation of Shanghai under Grant 17ZR1445200.

Publisher Copyright:
© 2004-2012 IEEE.


  • empirical necessary condition
  • Network controllability
  • node degree
  • optimization
  • robustness


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