Analysis of critical and redundant nodes in controlling directed and undirected complex networks using dominating sets

Journal of Complex Networks

Volumn 2, Issue 4, 2014, Pages 394-412

  Nacher, Jose C ^a   Akutsu, Tatsuya ^b  

^a TOHO UNIVERSITY   (Japan)

^b KYOTO UNIVERSITY   (Japan)

Author keywords

Complex networks; Controllability; Dominating sets

Indexed keywords

CONTROLLABILITY; DIRECTED GRAPHS; FUNCTIONS;

ALGORITHMIC PROCEDURE; ANALYSIS AND SIMULATION; ANALYTICAL EXPRESSIONS; CENTRALIZED CONTROL; COMPUTATIONAL EXPERIMENT; DOMINATING SETS; MATHEMATICAL ANALYSIS; MINIMUM DOMINATING SET;

COMPLEX NETWORKS;

EID: 84922774376     PISSN: 20511310     EISSN: 20511329     Source Type: Journal    
DOI: 10.1093/comnet/cnu029     Document Type: Article

References (35)

1. Newman, M. E. J., Barabási, A.-L. & Watts, D. J. (2006) The Structure and Dynamics of Networks. New York: Princeton University Press.
2. Newman, M. E. J. (2010) Networks: An Introduction. New York: Oxford University Press.
3. Nacher, J. C. & Ochiai T. (2008) Power-law distribution of gene expression fluctuations. Phys. Lett. A, 372, 6202-6206.
4. Lombardi, A. & Hornquist, M. (2007) Controllability analysis of networks. Phys. Rev. E., 75, 56110.
5. Kailath, T. (1980) Linear Systems. New York: Prentice Hall.
6. Kalman, R. E. (1963) Mathematical description of linear dynamics systems. Japan J. Indust. Appl. Math. A, 1, 152-192.
7. Luenberger, D. G. (1979) Introduction to Dynamic Systems: Theory, Models, & Applications. New York: John Wiley & Sons.
8. Akutsu, T., Hayashida, M., Ching, W.-K. & Ng, M. K. (2007) Control of Boolean networks: hardness results and algorithms for tree structured networks. J. Theoret. Biol., 244, 670-679.
9. Liu, B, Chu, T., Wang, L., & Xie G. (2008) Controllability of a leader-follower dynamic network with switching topology. IEEE Trans. Automat. Control, 53, 1009-1013.
10. Rahmani, A., Ji, M., Mesbahi, M. & Egerstedt, M. (2009) Controllability of multi-agent systems from a graph-theoretic perspective. SIAM J. Contr. Optim., 48, 162-189.
11. Kim, D.-H. & Motter, A. E. (2009) Slave nodes and the controllability of metabolic networks. New J. Phys., 11, 113047.
12. Liu, Y.-Y., Slotine, J.-J. & Barabási, A.-L. (2011) Controllability of complex networks. Nature, 473, 167-173.
13. Cowan, N. J., Chastain, E. J., Vilhena, D. A., Freudenberg, J. S. & Bergstrom, C. T. (2012) Nodal dynamics, not degree distributions, determine the structural controllability of complex networks. PLoS ONE, 7, e38398.
14. Liu, Y.-Y., Slotine, J.-J. & Barabási, A.-L. (2013) Observability of complex systems. Proc. Natl. Acad. Sci. USA, 110, 2460-2465.
15. Wang, W.-X., Ni, X., Lai, Y.-C. & Grebogi, C. (2012) Optimizing controllability of complex networks by minimum structural perturbations. Phys. Rev. E, 85, 026115.
16. Yan, G., Ren, J., Lai, Y.-C, Lai, C.-H. & Li, B. (2012) Controlling complex networks: how much energy is needed? Phys. Rev. Lett., 108, 218703.
17. Jia, T & Barabási, A.-L. (2013) Control capacity and a random sampling method in exploring controllability of complex networks. Sci. Rep., 3, 2354.
18. Posfai, M., Liu, Y.-Y., Slotine, J.-J. & Barabási, A.-L. (2013) Effect of correlations on network controllability. Sci. Rep., 3, 1067.
19. Nacher, J. C. & Akutsu, T. (2012) Dominating scale-free networks with variable scaling exponent: heterogeneous networks are not difficult to control. New J. Phys., 14, 073005.
20. Nacher, J. C. & Akutsu, T. (2013) Analysis on controlling complex networks based on dominating sets. J. Phys.: Conf. Ser., 410, 012104.
21. Nacher, J. C. & Akutsu, T. (2013) Structural controllability of unidirectional bipartite networks. Sci. Rep., 3, 1647.
22. Stojmenovic, I., Seddigh, M. & Zunic, J. (2002) Dominating sets and neighbor elimination-based broadcasting algorithms in wireless networks. IEEE Trans. Parallel Distrib. Syst., 13, 14-25.
23. Haynes, T. W., Hedetniemi, S. T. & Slater, P. J. (1998) Fundamentals of Domination in Graphs. Pure Applied Mathematics. New York: Chapman and Hall/CRC.
24. Molnár, F., Sreenivasan, S., Szymanski, B. K. & Korniss, G. (2013) Minimum dominating sets in scalefree network ensembles. Sci. Rep., 3, 1736.
25. Wuchty, S. (2014) Controllability in protein interaction networks. Proc. Natl. Acad. Sci. USA, 111, 7156- 7160.
26. Jia, T., Liu, Y.-Y., Csokam, E., Posfai, M., Slotine, J.-J. & Barabási, A.-L. (2013) Emergence of bimodality in controlling complex networks. Nat. Commun., 4, 2002.
27. Viger, F. & Latapy, M. (2005) Efficient and simple generation of random simple connected graphs with prescribed degree sequence. Proceedings of the 11th International Computing and Combinatorics Conference (COCOON'05), pp. 440-449.
28. Nacher, J. C. & Akutsu, T. (2013) Analysis on critical nodes in controlling complex networks using dominating sets. Proceedings of the International Conference on Signal-Image Technology & Internet-Based Systems (SITIS 2013), pp. 649-654.
29. Garey, M. R. & Johnson, D. S. (1979) Computers and Intractability: A Guide to the Theory of NPCompleteness. New York: W.H. Freeman & Co.
30. Mitzenmacher, M. & Upfal, E. (2005) Probability and Computing. Randomized Algorithms and Probabilistic Analysis. Cambridge: Cambridge University Press.
31. Colizza, V., Pastor-Satorras, R. & Vespignani, A. (2007) Reaction-diffusion processes and metapopulation models in heterogenous networks. Nat. Phys., 3, 276-282.
32. The Database of Interacting Proteins (DIPS) http://dip.doe-mbi.ucla.edu/dip/.
33. Rosato, V., Issacharoff, L., Tiriticco, F., & Meloni, S. (2008) Modelling interdependent infrastructures using interacting dynamical models. Int. J. Crit. Infrastruct., 4, 63-79.
34. Milo, R., et al. (2002) Network motifs: Simple building blocks of complex networks. Science, 298, 824-828.
35. Melian, C. J. & Bascompte, J. (2004) Food web cohesion. Ecology, 85, 352-358.