Network structure of multivariate time series

Scientific Reports

Volumn 5, Issue , 2015, Pages

  Lacasa, Lucas ^a   Nicosia, Vincenzo ^a   Latora, Vito ^a  

^a QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84944909556     PISSN: None     EISSN: 20452322     Source Type: Journal    
DOI: 10.1038/srep15508     Document Type: Article

References (51)

1. Kantz, H. & Schreiber, T. Nonlinear Time Series Analysis (Cambridge University Press, Cambridge, 2006).
2. Hastie, T., Tibshirani, R. & Friedman, J. Elements of Statistical Learning (Springer-Verlag, 2009).
3. Albert, R. & Barabasi, A.-L. Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47 (2002).
4. Boccaletti, S., Latora, V., Moreno, Y., Chavez, M. & Hwang, D. U. Complex networks: structure and dynamics. Phys. Rep. 424, 175 (2006).
5. Newman, M. E. J. Networks: An Introduction. (Oxford University Press, Oxford, 2010).
6. Bullmore, E. & Sporns, O. Complex brain networks: graph theoretical analysis of structural and functional systems. Nat. Rev. Neurosci 10(3), 186-198 (2009).
7. Tumminello, M., Lillo, F. & Mantegna, R. N. Correlation, hierarchies, and networks in financial markets. Journal of Economic Behavior & Organization. 75(1), 40-58 (2010).
8. Cai, S.-M., Zhou, Y.-B., Zhou, T. & Zhou, P.-L. Hierarchical organization and disassortative mixing of correlation-based weighted financial networks. Int. J. Mod. Phys. C 21(3), 433-441 (2010).
9. Gao, Y.-C., Zeng, Y. & Cai, S.-M. Influence network in the Chinese stock market. J. Stat. Mech. P03017 (2015).
10. Zhang, J. & Small, M. Complex network from pseudoperiodic time series: topology versus dynamics. Phys. Rev. Lett. 96, 238701 (2006).
11. Kyriakopoulos, F. & Thurner, S. Directed network representations of discrete dynamical maps. In Lecture Notes in Computer Science 4488, 625-632 (2007).
12. Xu, X., Zhang, J. & Small, M. Superfamily phenomena and motifs of networks induced from time series. Proc. Natl. Acad. Sci. USA 105, 19601-19605 (2008).
13. Donner, R. V., Zou, Y., Donges, J. F., Marwan, N. & Kurths, J. Recurrence networks: a novel paradigm for nonlinear time series analysis. New J. Phys. 12, 033025 (2010).
14. Donner, R. V. et al. The Geometry of Chaotic Dynamics-A Complex Network Perspective. Eur. Phys. J. B 84, 653-672 (2011).
15. Lacasa, L., Luque, B., Ballesteros, F., Luque, J. & Nuno, J. C. From time series to complex networks: The visibility graph. Proc. Natl. Acad. Sci. USA 105, 13 (2008).
16. Luque, B., Lacasa, L., Luque, J. & Ballesteros, F. J. Horizontal visibility graphs: Exact results for random time series. Phys. Rev. E 80, 046103 (2009).
17. Lacasa, L. On the degree distribution of horizontal visibility graphs associated to Markov processes and dynamical systems: diagrammatic and variational approaches. Nonlinearity 27, 2063-2093 (2014).
18. Gutin, G., Mansour, M. & Severini, S. A characterization of horizontal visibility graphs and combinatorics on words. Physica A 390, 12 (2001).
19. Lacasa, L., Luque, B., Luque, J. & Nuño, J. C. The Visibility Graph: a new method for estimating the Hurst exponent of fractional Brownian motion. Europhys. Lett. 86, 30001 (2009).
20. Lacasa, L. & Toral, R. Description of stochastic and chaotic series using visibility graphs. Phys. Rev. E 82, 036120 (2010).
21. Luque, B., Lacasa, L., Ballesteros, F. J. & Robledo, A. Analytical properties of horizontal visibility graphs in the Feigenbaum scenario. Chaos 22, 013109 (2012).
22. Luque, B., Ballesteros, F. J., Nunez, A. M. & Robledo, A. Quasiperiodic graphs: structural design, scaling and entropic properties. J. Nonlin. Sci. 23 335-342 (2013).
23. Nunez, A., Luque, B., Lacasa, L., Gomez, J. P. & Robledo, A. Horizontal Visibility graphs generated by type-I intermittency. Phys. Rev. E 87, 052801 (2013).
24. Ahmadlou, M. & Adeli, H. Visibility graph similarity: A new measure of generalized synchronization in coupled dynamic systems. Physica D 241(4), 326-332 (2012).
25. Aguilar-San Juan, B. & Guzman-Vargas, L. Earthquake magnitude time series: scaling behavior of visibility networks. Eur. Phys. J. B. 86, 454 (2013).
26. Donner, R. V. & Donges, J. F. Visibility graph analysis of geophysical time series: Potentials and possible pitfalls. Acta Geophysica 60, 589-623 (2012).
27. Zou, Y., Small, M., Liu, Z. & Kurths, J. Complex network approach to characterize the statistical features of the sunspot series. New J. Phys. 16, 013051 (2014).
28. Zou, Y., Donner, R. V., Marwan, N., Small, M. & Kurths, J. Long-term changes in the north-south asymmetry of solar activity: a nonlinear dynamics characterization using visibility graphs. Nonlin. Processes Geophys. 21, 1113-1126 (2014).
29. Qian, M. C., Jiang, Z. Q. & Zhou, W. X. Universal and nonuniversal allometric scaling behaviors in the visibility graphs of world stock market indices. J. Phys. A 43, 335002 (2010).
30. Ahmadlou, M., Ahmadi, K., Rezazade, M. & Azad-Marzabadi, E. Global organization of functional brain connectivity in methamphetamine abusers. Clinical Neurophysiology 124, 6, 1122 (2013).
31. Nuñez, A., Lacasa, L. & Luque, B. Visibility algorithms: a short review in Graph Theory (Intech) (2012).
32. Bianconi, G. Statistical mechanics of multiplex networks: Entropy and overlap. Phys. Rev. E. 87, 062806 (2013).
33. Nicosia, V., Bianconi, G., Latora, V. & Barthelemy, M. Growing multiplex networks. Phys. Rev. Lett. 111, 058701 (2013).
34. De Domenico, M. et al. Mathematical formulation of multilayer networks. Phys. Rev. X 3, 041022 (2013).
35. Kivelä, M. et al. Multilayer networks. J. Complex Networks, 2(3), 203-271 (2014).
36. Boccaletti, S. et al. The structure and dynamics of multilayer networks. Phys. Rep. 544(1), 1-122 (2014).
37. Battiston, F., Nicosia, V. & Latora, V. Structural measures for multiplex networks. Phys. Rev. E 89, 032804 (2014).
38. Nicosia, V., Bianconi, G., Latora, V. & Barthelemy, M. Non-linear growth and condensation in multiplex networks. Phys. Rev. E 90, 042807 (2014).
39. Nicosia, V. & Latora, V. Measuring and modelling correlations in multiplex networks. arxiv:1403.1546 (2014).
40. Lacasa, L., Nuñez, A., Roldan, E., Parrondo, J. M. R. & Luque, B. Time series irreversibility: a visibility graph approach. Eur. Phys. J. B 85, 217 (2012).
41. Donges, J. F., Donner, R. V. & Kurths, J. Testing time series irreversibility using complex network methods. Europhys. Lett. 102, 10004 (2013).
42. L. Lacasa & R. Flanagan Time reversibility from visibility graphs of non-stationary time series. Phys. Rev. E 92, 022817 (2015).
43. Granger, C. W. J. Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37(3), 424-438 (1969).
44. Sporns, O. Structure and function of complex brain networks. Dialogues Clin. Neurosci. 15(3), 247-262 (2013).
45. Kaneko, K. Pattern dynamics in spatiotemporal chaos: Pattern selection, diffusion of defect and pattern competition intermettency. Physica D 34, 1-41 (1989).
46. Kaneko, K. Theory and applications of coupled map lattices (Vol. 12). John Wiley & Son Ltd. (1993).
47. Hilgers, A. & Beck, C., Hierarchical coupled map lattices as cascade models for hydrodynamic turbulence. Europhys. Lett. 45, 552 (1999).
48. Hilgers, A. & Beck, C. Turbulent behavior of stock market indices and foreign currency exchange rates. Int. J. Bif. Chaos 7, 1855 (1997).
49. Bevers, M. & Flather, C. H. Numerically exploiting habitat fragmentation effects on populations using cell-based coupled map lattices, Theor. Pop. Biol. 55, 61 (1999).
50. Beck, C. Chaotic scalar fields as models for dark energy. Phys. Rev. D 69(12), 123515 (2004).
51. Mantegna, R. Hierarchical structure in financial markets. Europhys J B. 11, 193-197 (1999).