title: Exact controllability of complex networks.
abstract: Controlling complex networks is of paramount importance in science and engineering. Despite the recent development of structural controllability theory, we continue to lack a framework to control undirected complex networks, especially given link weights. Here we introduce an exact controllability paradigm based on the maximum multiplicity to identify the minimum set of driver nodes required to achieve full control of networks with arbitrary structures and link-weight distributions. The framework reproduces the structural controllability of directed networks characterized by structural matrices. We explore the controllability of a large number of real and model networks, finding that dense networks with identical weights are difficult to be controlled. An efficient and accurate tool is offered to assess the controllability of large sparse and dense networks. The exact controllability framework enables a comprehensive understanding of the impact of network properties on controllability, a fundamental problem towards our ultimate control of complex systems.
authors.affiliation: School of Systems Science, Beijing Normal University, Beijing 100875, China.
authors.forename: Zhengzhong
authors.initials: Z
authors.lastname: Yuan
authors.forename: Chen
authors.initials: C
authors.lastname: Zhao
authors.forename: Zengru
authors.initials: Z
authors.lastname: Di
authors.forename: Wen-Xu
authors.initials: WX
authors.lastname: Wang
authors.forename: Ying-Cheng
authors.initials: YC
authors.lastname: Lai
references.citation: Nature. 2011 May 12;473(7346):167-73
references.pmid: 21562557
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Apr;75(4 Pt 2):046103
references.pmid: 17500957
references.citation: Science. 1999 Oct 15;286(5439):509-12
references.pmid: 10521342
references.citation: Biol Cybern. 2005 Jan;92(1):38-53
references.pmid: 15650898
references.citation: Phys Rev Lett. 2001 Apr 2;86(14):3200-3
references.pmid: 11290142
references.citation: Proc Natl Acad Sci U S A. 2000 Oct 10;97(21):11149-52
references.pmid: 11005838
references.citation: Proc Natl Acad Sci U S A. 2002 Feb 19;99 Suppl 1:2566-72
references.pmid: 11875211
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Feb;85(2 Pt 2):026115
references.pmid: 22463287
references.citation: Nature. 1998 Jun 4;393(6684):440-2
references.pmid: 9623998
references.citation: Nature. 2010 Apr 8;464(7290):890-3
references.pmid: 20376149
references.citation: Phys Rev Lett. 2012 May 25;108(21):218703
references.pmid: 23003312
references.citation: Nature. 2005 Jun 9;435(7043):814-8
references.pmid: 15944704
references.citation: Nature. 2000 Jul 27;406(6794):378-82
references.pmid: 10935628
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2007 May;75(5 Pt 2):056110
references.pmid: 17677136
references.citation: Nature. 2001 May 3;411(6833):41-2
references.pmid: 11333967
references.citation: Phys Rev Lett. 2000 Nov 20;85(21):4626-8
references.pmid: 11082612
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Jun;69(6 Pt 2):066133
references.pmid: 15244693
references.citation: PLoS One. 2012;7(9):e44459
references.pmid: 23028542