The interaction of distinct units in physical, social, biological and technological systems naturally gives rise to complex network structures. Networks have constantly been in the focus of research for the past decade, with considerable advances in the description of their structural and dynamical properties. However, much less effort has been devoted to studying the controllability of the dynamics taking place on them. Here we introduce and evaluate a dynamical process defined on the edges of a network, and demonstrate that the controllability properties of this process significantly differ from simple nodal dynamics. Evaluation of real-world networks indicates that most of them are more controllable than their randomized counterparts. We also find that transcriptional regulatory networks are particularly easy to control. Analytic calculations show that networks with scale-free degree distributions have better controllability properties than uncorrelated networks, and positively correlated in- and out-degrees enhance the controllability of the proposed dynamics.
At a glance
- The structure and function of complex networks. SIAM Rev. 45, 167–256 (2003).
- Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002). &
- Complex networks: Structure and dynamics. Phys. Rep. 424, 175–308 (2006). , , , &
- Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998). &
- Emergence of scaling in random networks. Science 286, 509–512 (1999). &
- Classes of small-world networks. Proc. Natl Acad. Sci. USA 97, 11149–11152 (2000). , , &
- Random graph models of social networks. Proc. Natl Acad. Sci. USA 99 (suppl 1), 2566–2572 (2002). , &
- & Proc. ACM SIGKDD Int. Conf. Knowledge Discovery and Data Mining (KDD, 2005).
- Community detection in graphs. Phys. Rep. 486, 75–174 (2010).
- Finding and evaluating community structure in networks. Phys. Rev. E 69, 026113 (2004). &
- Uncovering the overlapping community structure of complex networks in nature and society. Nature 435, 814–818 (2005). , , &
- Dynamics of social networks. Complexity 8, 24–27 (2002). , &
- Genomic analysis of regulatory network dynamics reveals large topological changes. Nature 431, 308–312 (2004). , , , , &
- Dynamic properties of network motifs contribute to biological network organization. PLoS Biol. 3, 1881–1892 (2005). , &
- Quantifying social group evolution. Nature 446, 664–667 (2007). , &
- On pinning synchronization of complex dynamical networks. Automatica 45, 429–435 (2009). , &
- Controllability analysis of networks. Phys. Rev. E 75, 056110 (2007). &
- Controllability of multi-agent systems from a graph-theoretic perspective. SIAM J. Contr. Optim. 48, 162–186 (2009). , , &
- Mathematical description of linear dynamical systems. J. Soc. Indus. Appl. Math. Ser. A 1, 152–192 (1963).
- 1998). Mathematical Control Theory (Springer,
- 1991). & Applied Nonlinear Control (Prentice-Hall,
- Controllability of complex networks. Nature 473, 167–173 (2011). , &
- Structural controllability. IEEE Trans. Automat. Contr. 19, 201–208 (1974).
- Structural controllability of multi-input linear systems. IEEE Trans. Automat. Contr. 21, 203–212 (1976). &
- Network motifs: Simple building blocks of complex networks. Science 298, 824–827 (2002). , , , , &
- Comprehensive analysis of combinatorial regulation using the transcriptional regulatory network of yeast. J. Mol. Biol. 360, 213–227 (2006). , , , &
- , , & Proc. Int. Telecommunications Society 14th Biennial Conference (ITS2002) (2002).
- Error and attack tolerance of complete networks. Nature 406, 378–382 (2000). , &
- Resilience of the Internet to random breakdowns. Phys. Rev. Lett. 85, 4626–4628 (2000). , , &
- Lethality and centrality in protein networks. Nature 411, 41–42 (2001). , , &
- Epidemic spreading in scale-free networks. Phys. Rev. Lett. 86, 3200–3203 (2001). &
- Immunization of complex networks. Phys. Rev. E 65, 036104 (2002). &
- 2004). & The Hidden Power of Social Networks (Harvard Business School Press,
- & Social Science Research Reports 46. Technical report (Univ. California, 1979).
- Fuzzy communities and the concept of bridgeness in complex networks. Phys. Rev. E 77, 016107 (2008). , , &
- Hierarchy measure for complex networks. PLoS ONE 7, e33799 (2012). , &
- Hierarchical group dynamics in pigeon flocks. Nature 464, 890–893 (2010). , , &
- 1361–1370 (ACM, 2010). , & Proc. ACM SIGCHI Conf. Human Factors in Computing Systems (CHI)
- On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci. 5, 17–60 (1960). &
- 2nd edn (Cambridge Univ. Press, 2001). Cambridge Studies in Advanced Mathematics
- C. elegans for Computation 1st edn (CRC Press, 1992). & AY’s Neuroanatomy of
- Directed network modules. New J. Phys. 9, 186 (2007). , , , &
- 2005). & Proc. WWW-2005 Workshop on the Weblogging Ecosystem (ACM,
- Diameter of the World Wide Web. Nature 401, 130–131 (1999). , &
- 2007). Scale-Free Networks: Complex Web in Nature and Technology (Oxford Univ. Press,
- Loops of any size and hamilton cycles in random scale-free networks. J. Stat. Mech.P06005 (2005). &
- Percolation in directed scale-free networks. Phys. Rev. E 66, 015104 (2002). , , , &
- 435–444 (ACM, 2006). , , , , , & Proc. 2006 ACM CIKM Int. Conf. Information and Knowledge Management
- Decoding the structure of the WWW: Comparative analysis of web crawls. ACM Trans. Web 1, 10 (2007). , , , &
- Local structure of directed networks. Phys. Rev. Lett. 100, 118701 (2008). , &
- Directedness of information flow in mobile phone communication networks. PLoS ONE 6, e28860 (2011). &
- Supplementary Information (1200kb)