title: Control capacity and a random sampling method in exploring controllability of complex networks.
abstract: Controlling complex systems is a fundamental challenge of network science. Recent advances indicate that control over the system can be achieved through a minimum driver node set (MDS). The existence of multiple MDS's suggests that nodes do not participate in control equally, prompting us to quantify their participations. Here we introduce control capacity quantifying the likelihood that a node is a driver node. To efficiently measure this quantity, we develop a random sampling algorithm. This algorithm not only provides a statistical estimate of the control capacity, but also bridges the gap between multiple microscopic control configurations and macroscopic properties of the network under control. We demonstrate that the possibility of being a driver node decreases with a node's in-degree and is independent of its out-degree. Given the inherent multiplicity of MDS's, our findings offer tools to explore control in various complex systems.
authors.affiliation: Center for Complex Network Research and Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA.
authors.forename: Tao
authors.initials: T
authors.lastname: Jia
authors.forename: Albert-László
authors.initials: AL
authors.lastname: Barabási
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D005246:Feedback; D015233:Models, Statistical
references.citation: Nature. 2011 May 12;473(7346):167-73
references.pmid: 21562557
references.citation: Nature. 1998 Jun 4;393(6684):440-2
references.pmid: 9623998
references.citation: Phys Rev Lett. 2012 May 25;108(21):218703
references.pmid: 23003312
references.citation: J Mol Biol. 2006 Jun 30;360(1):213-27
references.pmid: 16762362
references.citation: Phys Rev Lett. 2008 Mar 21;100(11):118701
references.pmid: 18517837
references.citation: Phys Rev Lett. 2013 May 17;110(20):208701
references.pmid: 25167459
references.citation: Nucleic Acids Res. 2008 Jan;36(Database issue):D120-4
references.pmid: 18158297
references.citation: Sci Rep. 2013;3:1067
references.pmid: 23323210
references.citation: Nature. 2000 Oct 5;407(6804):651-4
references.pmid: 11034217
references.citation: Proc Natl Acad Sci U S A. 2013 Feb 12;110(7):2460-5
references.pmid: 23359701
references.citation: Proc Natl Acad Sci U S A. 2011 Sep 6;108(36):15004-9
references.pmid: 21873252
references.citation: PLoS One. 2012;7(9):e44459
references.pmid: 23028542
references.citation: Proc Natl Acad Sci U S A. 2011 Oct 18;108(42):17257-62
references.pmid: 21911407
references.citation: Science. 2002 May 3;296(5569):910-3
references.pmid: 11988575
references.citation: Proc Natl Acad Sci U S A. 2004 Oct 5;101(40):14333-7
references.pmid: 15448210
references.citation: Phys Rev Lett. 2001 Dec 31;87(27 Pt 1):278701
references.pmid: 11800921
references.citation: Sci Rep. 2012;2:469
references.pmid: 22741058
references.citation: Annu Rev Biochem. 1993;62:323-48
references.pmid: 8352593
references.citation: Nat Commun. 2013;4:2002
references.pmid: 23774965
references.citation: PLoS One. 2012;7(7):e41375
references.pmid: 22848475
references.citation: Science. 2002 Aug 30;297(5586):1551-5
references.pmid: 12202830
references.citation: Sci Rep. 2012;2:396
references.pmid: 22563525
references.citation: Science. 2004 Mar 5;303(5663):1538-42
references.pmid: 15001784
references.citation: Science. 1999 Oct 15;286(5439):509-12
references.pmid: 10521342
references.citation: Sci Rep. 2013;3:1626
references.pmid: 23568033
references.citation: Sci Rep. 2013;3:1647
references.pmid: 23571689
references.citation: Phys Rev Lett. 2001 Dec 17;87(25):258701
references.pmid: 11736611
references.citation: Int Rev Cytol Suppl. 1983;15:49-89
references.pmid: 6343284
references.citation: PLoS One. 2010 Dec 02;5(12):e14139
references.pmid: 21152034
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Feb;85(2 Pt 2):026115
references.pmid: 22463287
references.citation: Proc Natl Acad Sci U S A. 2002 Oct 1;99(20):12917-22
references.pmid: 12235364
references.citation: PLoS One. 2012;7(6):e38398
references.pmid: 22761682
references.citation: Science. 2002 Oct 25;298(5594):824-7
references.pmid: 12399590