title: Estimating the minimum control count of random network models.
abstract: The study of controllability of complex networks has introduced the minimum number of controls required for full controllability as a new network measure of interest. This network measure, like many others, is non-trivial to compute. As a result, establishing the significance of minimum control counts (MCCs) in real networks using random network null models is expensive. Here we derive analytic estimates for the expected MCCs of networks drawn from three commonly-used random network models. Our estimates show good agreement with exact control counts. Furthermore, the analytic expressions we derive offer insights into the structures within each random network model that induce the need for controls.
authors.affiliation: School of Computer Science, McGill University, Montreal, Canada.
authors.forename: Derek
authors.initials: D
authors.lastname: Ruths
authors.affiliation: Engineering Systems and Design, Singapore University of Technology and Design, Singapore.
authors.forename: Justin
authors.initials: J
authors.lastname: Ruths
references.citation: PLoS One. 2012;7(9):e44459
references.pmid: 23028542
references.citation: Science. 2002 Oct 25;298(5594):824-7
references.pmid: 12399590
references.citation: Science. 1999 Oct 15;286(5439):509-12
references.pmid: 10521342
references.citation: Nat Commun. 2013;4:2002
references.pmid: 23774965
references.citation: Science. 2014 Mar 21;343(6177):1373-6
references.pmid: 24653036
references.citation: Phys Rev Lett. 2012 May 25;108(21):218703
references.pmid: 23003312
references.citation: Proc Natl Acad Sci U S A. 2011 Mar 8;108(10):3838-41
references.pmid: 21368159
references.citation: Phys Rev Lett. 2013 May 17;110(20):208701
references.pmid: 25167459
references.citation: PLoS One. 2012;7(6):e38398
references.pmid: 22761682
references.citation: Nature. 2011 May 12;473(7346):167-73
references.pmid: 21562557
references.citation: BMC Bioinformatics. 2012;13:318
references.pmid: 23194062
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Feb;83(2 Pt 2):025102
references.pmid: 21405879
references.citation: Sci Rep. 2013;3:1067
references.pmid: 23323210