Network structures and systems: II. Network and multiplex cores
DOI:
https://doi.org/10.20535/SRIT.2308-8893.2018.3.04Keywords:
complex network, network system, flow, multiplex, model, core, kernelAbstract
The notion of the flow core of the network system is introduced and the functional advantages of its structure in comparison with the core of the complex network are analyzed. It has been shown that the flow cores allow us to construct a much more adequate with functional point of view the models of network systems than the cores of complex networks. This is demonstrated on the examples of practically important problems of controllability, observability and synchronization of complex networks. On the base of analysis of the structures of real systems, a generalized definition of the multiplex is proposed and the notion of its kernel is introduced. A few of modeling problems of multiplexes are considered and it is established that the effect of the "small world" in them increases. The flow adjacency matrix for the multiplex system is constructed. On its basis, a few of local and global characteristics of the multiplex system are determined and the properties of its flow core are investigated. Methods of reducing the dimension of models of multiplex systems with simultaneous monitoring of the quantitative measure of maintaining their adequacy are analyzed.References
Barabási A.-L. Linked: the new science of networks / A.-L. Barabási, J. Frangos. — New York: Basic Books, 2002. — 280 p.
Polishchuk O. Issues of regional development and evaluation problems / O. Polishchuk, D. Polishchuk, M. Tyutyunnyk, M. Yadzhak // AASCIT Communications. — 2015. — Vol. 2 (4). — P. 115–120.
Polishchuk D. Solution of some problems of evaluation of the complex systems / D. Polishchuk, O. Polishchuk, M. Yadzhak // Proc. of the 15th Int. conf. on automatic control, 23–26 September 2008. — Odesa: ONMA. — P. 968–976.
Polishchuk O.D. Merezhevi struktury ta systemy: I. Potokovi kharakterystyky skladnykh merezh / O.D. Polishchuk, M.S. Jadzhak // Systemni doslidzhennja ta informatsijni tekhnolohiyi. — 2018. — № 2. – S. 42–54.
Dorogovtsev S.N. k-core organization of complex networks / S.N. Dorogovtsev, A.V. Goltsev, J.F.F. Mendes // Physical review letters. — 2006. — Vol. 96(4). — 040601. DOI: https:// doi.org/10.1103/PhysRevLett.96.040601.
Alvarez-Hamelin J.I. k-core decomposition: A tool for the visualization of large scale networks / J.I. Alvarez-Hamelin, L. Dall'Asta, A. Barrat, A. Vespignani // arXiv preprint. — arXiv: 0504107 [cs]. — 28 Apr 2005. — 13 p.
Scott W.R. Organizations and organizing: Rational, natural and open systems perspectives / W.R. Scott, G.F. Davis. — London: Routledge, 2015. — 464 p.
Boccaletti S. Structure and Dynamics of Multilayer Networks / S. Boccaletti, G. Bianconi, R. Criado et al. // Physics Reports. — 2014. — Vol. 544(1). — P. 1–122. DOI: https://doi.org/10.1016/j.physrep. 2014.07.001.
Corominas-Murtra B. Detection of the elite structure in a virtual multiplex social system by means of a generalised K-core / B. Corominas-Murtra, B. Fuchs, S. Thurner // PloS one. — 2014. — Vol. 9 (12). — e112606. DOI: http://dx.doi.org/10.1371/journal.pone.0112606.
Azimi-Tafreshi N. k−core percolation on multiplex networks / N. Azimi-Tafreshi, J. Gómez-Gardeñes, S.N. Dorogovtsev // Physical Review E. — 2014. — Vol. 90. — 032816. DOI: https: //doi.org/10.1103/PhysRevE.90.032816.
Holovach Ju. Skladni merezhi / Ju. Holovach, O. Olyemskoj, K. fon Ferber ta in. // Zhurnal fizychnykh doslidzhen'. — 2006. — 10, №4. — S. 247–289.
Polishchuk D.O. Monitorynh potoku transportnykh merezh iz chastkovo vporjadkovanym rukhom / D.O. Polishchuk, O.D. Polishchuk // KhKhIII nauk.-tekhn. konf. molodykh naukovtsiv Fizyko-mekhanichnoho instytutu im. H.V. Karpenka NANU: zb. nauk. prats'. — 23–25 zhovt., 2013. — L'viv. — S. 326–329.
Liu Y.-Y. Controllability of complex networks / Y.-Y. Liu, J.-J. Slotine, A.-L. Barabaґsi // Nature. — 2011. — Vol. 473. — P. 167–173. DOI: https://doi.org/10.1038/nature10011.
Liu Y.-Y. Observability of complex systems / Y.-Y. Liu, J.J. Slotine, A.L. Barabási // Proc. of the National Academy of Sciences. — 2013. — Vol. 110(7). — P. 2460–2465. DOI: https://doi.org/ 10.1073/pnas.1215508110.
Novikov A.V. Oscillatory neural networks based on the Kuramoto model for cluster analysis / A.V. Novikov, E.N. Benderskaya // Pattern Recognition and Image Analysis. — 2014. — Vol. 24(3). — P. 365–371. DOI: https://doi.org/10. 1134/S1054661814030146.
Buldyrev S.V. Catastrophic cascade of failures in interdependent networks / S.V. Buldyrev, R. Parshani, G. Paul et al. // Nature. — 2010. — Vol. 464(15). — P. 1025–1028. DOI: https://doi.org/10.1038/nature08932.
Lombardi A. Controllability analysis of networks / A. Lombardi, M. Hörnquist // Physical Review E. — 2007. — Vol. 75(5). — 056110. DOI: https://doi.org /10.1103/PhysRevE.75. 056110.
Sedoglavic A. A probabilistic algorithm to test local algebraic observability in polynomial time / A. Sedoglavic // Proc. of the 2001 Intern. Symp. on Symbolic and algebraic computation. — 23–29 July 2001. — P. 309–317. DOI: https://doi.org/10.1145/384101.384143.
Gomez-Gardennes J. Paths synchronization on complex networks / J. Gomez-Gardennes, Y. Moreno, A. Arenas // Physical Review Letters. — 2007. — Vol. 98. — 034101. DOI: https:// doi.org/10.1103/PhysRevLett.98.034101.
Kuramoto Y. Chemical oscillations waves, and turbulence / Y. Kuramoto. — Berlin: Springer-Verlag, 1984. — 157 p.
Daido H. Quasientrainment and slow relaxation in a population of oscillators with random and frustrated interactions / H. Daido // Physical Review Letters. — 1992. — Vol. 73. — P. 1073–1076. DOI: https://doi.org/10.1103/ PhysRevLett.68.1073.
Polishchuk O. Flows characteristics and cores of complex network and multiplex type systems / O. Polishchuk // arXiv preprint. — arXiv:1702.02730 [physics.soc-ph]. — 9 Feb 2017. — 22 p.
Polishchuk D. Global network structures and problems of aggregative evaluations / D. Polishchuk, O. Polishchuk // International frontier science letters. — 2016. — Vol. 8. — P. 31–45. DOI: http://doi.org/10.18052/www.scipress.com/IFSL.8.31.
