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1. R. Albert and A. L. Barabási, “ Statistical mechanics of complex networks,” Rev. Mod. Phys. 74, 4797 (2002).
2. M. E. J. Newman, “ The structure and function of complex networks,” SIAM Rev. 45, 167256 (2003).
3. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-U. Hwang, “ Complex networks: Structure and dynamics,” Phys. Rep. 424, 175308 (2006).
4. R. Cohen and S. Havlin, Complex Networks: Structure, Robustness and Function ( Cambridge University Press, Cambridge, 2010).
5. M. E. J. Newman, Networks: An Introduction ( Oxford University Press, Oxford, 2010).
6. H. D. I. Abarbanel, Analysis of Observed Chaotic Data ( Springer, New York, 1996).
7. J. C. Sprott, Chaos and Time-Series Analysis ( Oxford University Press, Oxford, 2003).
8. H. Kantz and T. Schreiber, Nonlinear Time Series Analysis, 2nd ed. ( Cambridge University Press, Cambridge, 2004).
9. G. Csárdi and T. Nepusz, “ The igraph software package for complex network research,” InterJ. Complex Syst. CX.18, 1695 (2006).
10. D. A. Schult and P. J. Swart, “ Exploring network structure, dynamics, and function using NetworkX,” in Proceedings of the 7th Python in Science Conferences (SciPy 2008) (2008), Vol. 2008, pp. 1116.
11. R. Hegger, H. Kantz, and T. Schreiber, “ Practical implementation of nonlinear time series methods: The TISEAN package,” Chaos 9, 413435 (1999).
12. C. Zhou, L. Zemanová, G. Zamora, C. C. Hilgetag, and J. Kurths, “ Hierarchical organization unveiled by functional connectivity in complex brain networks,” Phys. Rev. Lett. 97, 238103 (2006).
13. C. Zhou, L. Zemanová, G. Zamora-Lopez, C. C. Hilgetag, and J. Kurths, “ Structure–function relationship in complex brain networks expressed by hierarchical synchronization,” New J. Phys. 9, 178 (2007).
14. E. Bullmore and O. Sporns, “ Complex brain networks: Graph theoretical analysis of structural and functional systems,” Nat. Rev. Neurosci. 10, 186198 (2009).
15. A. A. Tsonis and P. J. Roebber, “ The architecture of the climate network,” Physica A 333, 497504 (2004).
16. A. A. Tsonis and K. L. Swanson, “ Topology and predictability of El Niño and La Niña networks,” Phys. Rev. Lett. 100, 228502 (2008).
17. K. Yamasaki, A. Gozolchiani, and S. Havlin, “ Climate networks around the globe are significantly affected by El Niño,” Phys. Rev. Lett. 100, 228501 (2008).
18. J. F. Donges, Y. Zou, N. Marwan, and J. Kurths, “ Complex networks in climate dynamics—Comparing linear and nonlinear network construction methods,” Eur. Phys. J. ST 174, 157179 (2009).
19. J. F. Donges, Y. Zou, N. Marwan, and J. Kurths, “ The backbone of the climate network,” Europhys. Lett. 87, 48007 (2009).
20. J. F. Donges, I. Petrova, A. Loew, N. Marwan, and J. Kurths, “ How complex climate networks complement eigen techniques for the statistical analysis of climatological data,” Clim. Dyn. (published online 2015).
21. W.-Q. Huang, X.-T. Zhuang, and S. Yao, “ A network analysis of the Chinese stock market,” Physica A 388, 29562964 (2009).
22. R. V. Donner, M. Small, J. F. Donges, N. Marwan, Y. Zou, R. Xiang, and J. Kurths, “ Recurrence-based time series analysis by means of complex network methods,” Int. J. Bifurcation Chaos 21, 10191046 (2011).
23. X. Xu, J. Zhang, and M. Small, “ Superfamily phenomena and motifs of networks induced from time series,” Proc. Natl. Acad. Sci. U.S.A. 105, 1960119605 (2008).
24. N. Marwan, J. F. Donges, Y. Zou, R. V. Donner, and J. Kurths, “ Complex network approach for recurrence analysis of time series,” Phys. Lett. A 373, 42464254 (2009).
25. R. V. Donner, Y. Zou, J. F. Donges, N. Marwan, and J. Kurths, “ Recurrence networks—A novel paradigm for nonlinear time series analysis,” New J. Phys. 12, 033025 (2010).
26. J. F. Donges, J. Heitzig, R. V. Donner, and J. Kurths, “ Analytical framework for recurrence network analysis of time series,” Phys. Rev. E 85, 046105 (2012).
27. G. Nicolis, A. Garciá Cantú, and C. Nicolis, “ Dynamical aspects of interaction networks,” Int. J. Bifurcation Chaos 15, 3467 (2005).
28. L. Lacasa, B. Luque, F. Ballesteros, J. Luque, and J. C. Nuno, “ From time series to complex networks: The visibility graph,” Proc. Natl. Acad. Sci. U.S.A. 105, 49724975 (2008).
29. R. V. Donner and J. F. Donges, “ Visibility graph analysis of geophysical time series: Potentials and possible pitfalls,” Acta Geophys. 60, 589623 (2012).
30. J. F. Donges, R. V. Donner, and J. Kurths, “ Testing time series irreversibility using complex network methods,” Europhys. Lett. 102, 10004 (2013).
31. N. P. Subramaniyam and J. Hyttinen, “ Characterization of dynamical systems under noise using recurrence networks: Application to simulated and EEG data,” Phys. Lett. A 378, 34643474 (2014).
32. N. P. Subramaniyam, J. F. Donges, and J. Hyttinen, “ Signatures of chaotic and stochastic dynamics uncovered with ε-recurrence networks,” Proc. R. Soc. A—Math. Phys. (in press).
33.See supplemental material at for a comprehensive pyunicorn API documentation and exemplary code.[Supplementary Material]
34. T. E. Oliphant, “ Python for scientific computing,” Comput. Sci. Eng. 9, 1020 (2007).
35. K. J. Millman and M. Aivazis, “ Python for scientists and engineers,” Comput. Sci. Eng. 13, 912 (2011).
36. F. Pérez and B. E. Granger, “ Ipython: A system for interactive scientific computing,” Comput. Sci. Eng. 9, 2129 (2007).
37. S. van der Walt, S. C. Colbert, and G. Varoquaux, “ The numpy array: A structure for efficient numerical computation,” Comput. Sci. Eng. 13, 2230 (2011).
38. E. Jones, T. Oliphant, and P. Peterson et al., “ SciPy: Open source scientific tools for Python,” 2001, Online, (accessed May 30, 2015).
39. J. D. Hunter, “ Matplotlib: A 2d graphics environment,” Comput. Sci. Eng. 9, 9095 (2007).
40. T. Nocke, S. Buschmann, J. F. Donges, N. Marwan, H.-J. Schulz, and C. Tominski, “ Review: Visual analytics of climate networks,” Nonlinear Proc. Geophys. 22, 545570 (2015).
41. C. Tominski, J. Abello, and H. Schumann, “ CGV–an interactive graph visualization system,” Comput. Graph. 33, 660678 (2009).
42. C. Tominski, J. F. Donges, and T. Nocke, “ Information visualization in climate research,” in 15th International Conference on Information Visualisation (IV) (IEEE, 2011), pp. 298305.
43. S. Behnel, R. Bradshaw, C. Citro, L. Dalcin, D. S. Seljebotn, and K. Smith, “ Cython: The best of both worlds,” Comput. Sci. Eng. 13, 3139 (2011).
44. M. E. J. Newman, “ A measure of betweenness centrality based on random walks,” Soc. Networks 27, 3954 (2005).
45. A. Arenas, A. Cabrales, A. Díaz-Guilera, R. Guimerà, and F. Vega-Redondo, “ Search and congestion in complex networks,” in Statistical Mechanics of Complex Networks, Lecture Notes in Physics Vol. 625, edited by R. Pastor-Satorras, M. Rubi, and A. Díaz-Guilera ( Springer, Berlin/Heidelberg, 2003), pp. 175194.
46. U. Brandes, M. Eiglsperger, I. Herman, M. Himsolt, and M. S. Marshall, “ GraphML progress report. Structural layer proposal,” in Proceedings 9th International Symposium on Graph Drawing (GD'01), edited by Department of Computer & Information Science, University of Konstanz, Germany (Springer, 2002), pp. 501512.
47. M. Bastian, S. Heymann, and M. Jacomy, “ Gephi: An open source software for exploring and manipulating networks,” in Proceedings of the International AAAI Conference on Weblogs and Social Media (2009).
48. M. Barthélemy, “ Spatial networks,” Phys. Rep. 499, 1101 (2011).
49. A. A. Tsonis, K. L. Swanson, and G. Wang, “ On the role of atmospheric teleconnections in climate,” J. Clim. 21, 29903001 (2008).
50. M. Wiedermann, J. F. Donges, J. Kurths, and R. V. Donner, “ Spatial network surrogates for disentangling complex system structure from spatial embedding of nodes,” preprint arXiv:150909293 (2015).
51. M. T. Gastner and M. E. J. Newman, “ The spatial structure of networks,” Eur. Phys. J. B 49, 247252 (2006).
52. J. F. Donges, H. C. H. Schultz, N. Marwan, Y. Zou, and J. Kurths, “ Investigating the topology of interacting networks—Theory and application to coupled climate subnetworks,” Eur. Phys. J. B 84, 635652 (2011).
53. M. Wiedermann, J. F. Donges, J. Heitzig, and J. Kurths, “ Node-weighted interacting network measures improve the representation of real-world complex systems,” Europhys. Lett. 102, 28007 (2013).
54. S. V. Buldyrev, R. Parshani, G. Paul, H. E. Stanley, and S. Havlin, “ Catastrophic cascade of failures in interdependent networks,” Nature 464, 10251028 (2010).
55. J. Gao, S. V. Buldyrev, H. E. Stanley, and S. Havlin, “ Networks formed from interdependent networks,” Nat. Phys. 8, 4048 (2012).
56. S. Boccaletti, G. Bianconi, R. Criado, C. Del Genio, J. Gómez-Gardeñes, M. Romance, I. Sendina-Nadal, Z. Wang, and M. Zanin, “ The structure and dynamics of multilayer networks,” Phys. Rep. 544, 1122 (2014).
57. M. Girvan and M. E. J. Newman, “ Community structure in social and biological networks,” Proc. Natl. Acad. Sci. U.S.A. 99, 78217826 (2002).
58. M. E. J. Newman, “ Modularity and community structure in networks,” Proc. Natl. Acad. Sci. U.S.A. 103, 85778582 (2006).
59. S. Fortunato, “ Community detection in graphs,” Phys. Rep. 486, 75174 (2010).
60. P. Erdős and A. Rényi, “ On random graphs I,” Publ. Math. Debrecen 6, 290297 (1959).
61. W. W. Zachary, “ An information flow model for conflict and fission in small groups,” J. Anthropol. Res. 33, 452473 (1977).
62. M. Wiedermann, J. F. Donges, D. Handorf, J. Kurths, and R. V. Donner, “ Hierarchical structures in northern hemispheric extratropical winter ocean-atmosphere interactions,” preprint arXiv:150606634 (2015).
63. J. H. Feldhoff, R. V. Donner, J. F. Donges, N. Marwan, and J. Kurths, “ Geometric detection of coupling directions by means of inter-system recurrence networks,” Phys. Lett. A 376, 35043513 (2012).
64. J. Heitzig, J. F. Donges, Y. Zou, N. Marwan, and J. Kurths, “ Node-weighted measures for complex networks with spatially embedded, sampled, or differently sized nodes,” Eur. Phys. J. B 85, 38 (2012).
65. A. Rheinwalt, N. Marwan, J. Kurths, P. Werner, and F.-W. Gerstengarbe, “ Boundary effects in network measures of spatially embedded networks,” Europhys. Lett. 100, 28002 (2012).
66. A. Radebach, R. V. Donner, J. Runge, J. F. Donges, and J. Kurths, “ Disentangling different types of El Niño episodes by evolving climate network analysis,” Phys. Rev. E 88, 052807 (2013).
67. N. Molkenthin, K. Rehfeld, V. Stolbova, L. Tupikina, and J. Kurths, “ On the influence of spatial sampling on climate networks,” Nonlinear Proc. Geophys. 21, 651657 (2014).
68. D. C. Zemp, M. Wiedermann, J. Kurths, A. Rammig, and J. F. Donges, “ Node-weighted measures for complex networks with directed and weighted edges for studying continental moisture recycling,” Europhys. Lett. 107, 58005 (2014).
69. D. C. Zemp, C.-F. Schleussner, H. M. J. Barbosa, R. J. Van der Ent, J. F. Donges, J. Heinke, G. Sampaio, and A. Rammig, “ On the importance of cascading moisture recycling in South America,” Atmos. Chem. Phys. 14, 1333713359 (2014).
70. J. H. Feldhoff, S. Lange, J. Volkholz, J. F. Donges, J. Kurths, and F.-W. Gerstengarbe, “ Complex networks for climate model evaluation with application to statistical versus dynamical modeling of South American climate,” Clim. Dyn. 44, 15671581 (2015).
71. S. Lange, J. F. Donges, J. Volkholz, and J. Kurths, “ Local difference measures between complex networks for dynamical system model evaluation,” PLoS ONE 10, e0118088 (2015).
72. A. Rheinwalt, N. Boers, N. Marwan, J. Kurths, P. Hoffmann, F.-W. Gerstengarbe, and P. Werner, “ Non-linear time series analysis of precipitation events using regional climate networks for Germany,” Clim. Dyn. (published online 2015).
73. N. Molkenthin, K. Rehfeld, N. Marwan, and J. Kurths, “ Networks from flows—From dynamics to topology,” Sci. Rep. 4, 4119 (2014).
74. T. M. Cover and J. A. Thomas, Elements of Information Theory ( John Wiley & Sons, Hoboken, 2006).
75. C. E. Shannon, “ A Mathematical Theory of Communication,” Bell Syst. Tech. J. 27, 379423 (1948).
76. M. Paluš, “ Coarse-grained entropy rates for characterization of complex time series,” Physica D 93, 6477 (1996).
77. K. Hlaváčková-Schindler, M. Paluš, M. Vejmelka, and J. Bhattacharya, “ Causality detection based on information-theoretic approaches in time series analysis,” Phys. Rep. 441, 146 (2007).
78. A. Kraskov, H. Stögbauer, and P. Grassberger, “ Estimating mutual information,” Phys. Rev. E 69, 066138 (2004).
79. J. Runge, J. Heitzig, N. Marwan, and J. Kurths, “ Quantifying causal coupling strength: A lag-specific measure for multivariate time series related to transfer entropy,” Phys. Rev. E 86, 061121 (2012).
80. J. Hlinka, D. Hartman, M. Vejmelka, J. Runge, N. Marwan, J. Kurths, and M. Palus, “ Reliability of inference of directed climate networks using conditional mutual information,” Entropy 15, 20232045 (2013).
81. T. Schreiber, “ Measuring information transfer,” Phys. Rev. Lett. 85, 461464 (2000).
82. B. Pompe and J. Runge, “ Momentary information transfer as a coupling measure of time series,” Phys. Rev. E 83, 051122 (2011).
83. S. Frenzel and B. Pompe, “ Partial mutual information for coupling analysis of multivariate time series,” Phys. Rev. Lett. 99, 204101 (2007).
84. J. Runge, V. Petoukhov, and J. Kurths, “ Quantifying the strength and delay of climatic interactions: The ambiguities of cross correlation and a novel measure based on graphical models,” J. Clim. 27, 720739 (2014).
85. M. Eichler, “ Graphical modelling of multivariate time series,” Probab. Theory Relat. Fields 153, 233268 (2012).
86. J. Runge, J. Heitzig, V. Petoukhov, and J. Kurths, “ Escaping the curse of dimensionality in estimating multivariate transfer entropy,” Phys. Rev. Lett. 108, 258701 (2012).
87. C.-F. Schleussner, J. Runge, J. Lehmann, and A. Levermann, “ The role of the North Atlantic overturning and deep ocean for multi-decadal global-mean-temperature variability,” Earth Syst. Dyn. 5, 103115 (2014).
88. G. Balasis, R. V. Donner, S. M. Potirakis, J. Runge, C. Papadimitriou, I. Daglis, K. Eftaxis, and J. Kurths, “ Statistical mechanics and information-theoretic perspectives on complexity in the Earth system,” Entropy 15, 48444888 (2013).
89. J. Runge, V. Petoukhov, J. F. Donges, J. Hlinka, N. Jajcay, M. Vejmelka, D. Hartman, N. Marwan, M. Paluš, and J. Kurths, “ Identifying causal gateways and mediators in complex spatio-temporal systems,” Nat. Commun. 6, 8502 (2015).
90. J. Runge, “ Quantifying information transfer and mediation along causal pathways in complex systems,” preprint arXiv:150803808 (2015).
91. J. F. Donges, “ Functional network macroscopes for probing past and present Earth system dynamics: Complex hierarchical interactions, tipping points, and beyond,” Ph.D. dissertation, Humboldt University, Berlin, Germany, 2012.
92. J. Ludescher, A. Gozolchiani, M. I. Bogachev, A. Bunde, S. Havlin, and H. J. Schellnhuber, “ Improved El Nino forecasting by cooperativity detection,” Proc. Natl. Acad. Sci. U.S.A. 110, 1174211745 (2013).
93. J. Ludescher, A. Gozolchiani, M. I. Bogachev, A. Bunde, S. Havlin, and H. J. Schellnhuber, “ Very early warning of next El Niño,” Proc. Natl. Acad. Sci. U.S.A. 111, 20642066 (2014).
94. H. Ihshaish, A. Tantet, J. C. M. Dijkzeul, and H. A. Dijkstra, “ Par@Graph—A parallel toolbox for the construction and analysis of large complex climate networks,” Geosci. Model Dev. 8, 33213331 (2015).
95. Q. Y. Feng and H. A. Dijkstra, “ Are North Atlantic multidecadal SST anomalies westward propagating?Geophys. Res. Lett. 41, 541546, doi:10.1002/2013GL058687 (2014).
96. M. Mheen, H. A. Dijkstra, A. Gozolchiani, M. den Toom, J. Feng, Q. Kurths, and E. Hernandez-Garcia, “ Interaction network based early warning indicators for the Atlantic MOC collapse,” Geophys. Res. Lett. 40, 27142719, doi:10.1002/grl.50515 (2013).
97. Q. Y. Feng, J. P. Viebahn, and H. A. Dijkstra, “ Deep ocean early warning signals of an Atlantic MOC collapse,” Geophys. Res. Lett. 41, 60096015, doi:10.1002/2014GL061019 (2014).
98. E. Hawkins, R. S. Smith, L. C. Allison, J. M. Gregory, T. J. Woollings, H. Pohlmann, and B. de Cuevas, “ Bistability of the Atlantic overturning circulation in a global climate model and links to ocean freshwater transport,” Geophys. Res. Lett. 38, L10605, doi:10.1029/2011GL047208 (2011).
99. T. M. Lenton, H. Held, E. Kriegler, J. W. Hall, W. Lucht, S. Rahmstorf, and H. J. Schellnhuber, “ Tipping elements in the Earth's climate system,” Proc. Natl. Acad. Sci. U.S.A. 105, 17861793 (2008).
100. F. O. Bryan, “ High-latitude salinity effects and interhemispheric thermohaline circulations,” Nature 323, 301304 (1986).
101. S. Rahmstorf, “ The thermohaline circulation: a system with dangerous thresholds?,” Clim. Change 46, 247256 (2000).
102. K. Rehfeld, N. Marwan, S. F. M. Breitenbach, and J. Kurths, “ Late Holocene Asian Summer Monsoon dynamics from small but complex networks of palaeoclimate data,” Clim. Dyn. 41, 319 (2013).
103. A. Gozolchiani, K. Yamasaki, O. Gazit, and S. Havlin, “ Pattern of climate network blinking links follows El Niño events,” Europhys. Lett. 83, 28005 (2008).
104. N. Malik, B. Bookhagen, N. Marwan, and J. Kurths, “ Analysis of spatial and temporal extreme monsoonal rainfall over South Asia using complex networks,” Clim. Dyn. 39, 971987 (2012).
105. V. Stolbova, P. Martin, B. Bookhagen, N. Marwan, and J. Kurths, “ Topology and seasonal evolution of the network of extreme precipitation over the Indian subcontinent and Sri Lanka,” Nonlinear Proc. Geophys. 21, 901917 (2014).
106. L. Tupikina, K. Rehfeld, N. Molkenthin, V. Stolbova, N. Marwan, and J. Kurths, “ Characterizing the evolution of climate networks,” Nonlinear Proc. Geophys. 21, 705711 (2014).
107. G. J. Huffman, D. T. Bolvin, E. J. Nelkin, D. B. Wolff, R. F. Adler, G. Gu, Y. Hong, K. P. Bowman, and E. F. Stocker, “ The TRMM multisatellite precipitation analysis (TMPA): Quasi-global, multiyear, combined-sensor precipitation estimates at fine scales,” J. Hydrometeorol. 8, 3855 (2007).
108.TRMM, “ TRMM data set,” 2012, Online, (accessed February 25, 2014).
109. R. Quian Quiroga, T. Kreuz, and P. Grassberger, “ Event synchronization: A simple and fast method to measure synchronicity and time delay patterns,” Phys. Rev. E 66, 041904 (2002).
110. N. Boers, A. Rheinwalt, B. Bookhagen, H. M. Barbosa, N. Marwan, J. Marengo, and J. Kurths, “ The South American rainfall dipole: A complex network analysis of extreme events,” Geophys. Res. Lett. 41, 73977405, doi:10.1002/2014GL061829 (2014).
111. R. Kistler, E. Kalnay, W. Collins, S. Saha, G. White, J. Woollen, M. Chelliah, W. Ebisuzaki, M. Kanamitsu, V. Kousky, H. V. D. Dool, R. Jenne, and M. Fiorino, “ The NCEP–NCAR 50–year reanalysis: Monthly means CD–ROM and documentation,” Bull. Am. Meteorol. Soc. 82, 247268 (2001).<0247:TNNYRM>2.3.CO;2
112. P. Holme and J. Saramäki, “ Temporal networks,” Phys. Rep. 519, 97125 (2012).
113. Y. Berezin, A. Gozolchiani, O. Guez, and S. Havlin, “ Stability of climate networks with time,” Sci. Rep. 2, 666 (2012).
114. J.-S. Kug, S.-I. Choi, J. A. An, F.-F. Jin, and A. T. Wittenberg, “ Warm pool and cold tongue El Niño events as simulated by the GFDL 2.1 coupled GCM,” J. Clim. 23, 12261239 (2010).
115. A. Feng, Z. Gong, Q. Wang, and G. Feng, “ Three-dimensional air–sea interactions investigated with bilayer networks,” Theor. Appl. Climatol. 109, 635643 (2012).
116. N. A. Rayner, D. E. Parker, E. B. Horton, C. K. Folland, L. V. Alexander, D. P. Rowell, E. C. Kent, and A. Kaplan, “ Global analyses of sea surface temperature, sea ice, and night marine air temperature since the late nineteenth century,” J. Geophys. Res. 108, 4407, doi:10.1029/2002JD002670 (2003).
117. S. M. Uppala, P. W. Kållberg, A. J. Simmons, U. Andrae, V. D. C. Bechtold, M. Fiorino, J. K. Gibson, J. Haseler, A. Hernandez, G. A. Kelly, X. Li, K. Onogi, S. Saarinen, N. Sokka, R. P. Allan, E. Andersson, K. Arpe, M. A. Balmaseda, A. C. M. Beljaars, L. V. D. Berg, J. Bidlot, N. Bormann, S. Caires, F. Chevallier, A. Dethof, M. Dragosavac, M. Fisher, M. Fuentes, S. Hagemann, E. Hólm, B. J. Hoskins, L. Isaksen, P. A. E. M. Janssen, R. Jenne, A. P. Mcnally, J.-F. Mahfouf, J.-J. Morcrette, N. A. Rayner, R. W. Saunders, P. Simon, A. Sterl, K. E. Trenberth, A. Untch, D. Vasiljevic, P. Viterbo, and J. Woollen, “ The ERA-40 re-analysis,” Q. J. R. Meteorol. Soc. 131, 29613012 (2005).
118. E. Ravasz and A.-L. Barabási, “ Hierarchical organization in complex networks,” Phys. Rev. E 67, 026112 (2003).
119. J. Dall and M. Christensen, “ Random geometric graphs,” Phys. Rev. E 66, 016121 (2002).
120. R. V. Donner, J. Heitzig, J. F. Donges, Y. Zou, N. Marwan, and J. Kurths, “ The geometry of chaotic dynamics – a complex network perspective,” Eur. Phys. J. B 84, 653672 (2011).
121. L. Lacasa, B. Luque, J. Luque, and J. C. Nuno, “ The visibility graph: A new method for estimating the Hurst exponent of fractional Brownian motion,” Europhys. Lett. 86, 30001 (2009).
122. N. Marwan, M. C. Romano, M. Thiel, and J. Kurths, “ Recurrence plots for the analysis of complex systems,” Phys. Rep. 438, 237329 (2007).
123. N. Marwan and J. Kurths, “ Complex network based techniques to identify extreme events and (sudden) transitions in spatio-temporal systems,” Chaos 25, 097609 (2015).
124. M. C. Romano, M. Thiel, J. Kurths, and C. Grebogi, “ Estimation of the direction of the coupling by conditional probabilities of recurrence,” Phys. Rev. E 76, 036211 (2007).
125. Y. Zou, M. C. Romano, M. Thiel, N. Marwan, and J. Kurths, “ Inferring indirect coupling by means of recurrences,” Int. J. Bifurcation Chaos 21, 10991111 (2011).
126. N. Marwan, “ A historical review of recurrence plots,” Eur. Phys. J. ST 164, 312 (2008).
127. G. M. Ramírez Ávila, A. Gapelyuk, N. Marwan, H. Stepan, J. Kurths, T. Walther, and N. Wessel, “ Classifying healthy women and preeclamptic patients from cardiovascular data using recurrence and complex network methods,” Auton. Neusci. 178, 103110 (2013).
128. J. F. Donges, R. V. Donner, N. Marwan, S. F. Breitenbach, K. Rehfeld, and J. Kurths, “ Non-linear regime shifts in Holocene Asian monsoon variability: Potential impacts on cultural change and migratory patterns,” Clim. Past 11, 709741 (2015).
129. N. H. Packard, J. P. Crutchfield, J. D. Farmer, and R. S. Shaw, “ Geometry from a time series,” Phys. Rev. Lett. 45, 712716 (1980).
130. E. N. Lorenz, “ Deterministic nonperiodic flow,” J. Atmos. Sci. 20, 130141 (1963).<0130:DNF>2.0.CO;2
131. S. Schinkel, N. Marwan, O. Dimigen, and J. Kurths, “ Confidence bounds of recurrence-based complexity measures,” Phys. Lett. A 373, 22452250 (2009).
132. Y. Zou, R. V. Donner, J. F. Donges, N. Marwan, and J. Kurths, “ Identifying complex periodic windows in continuous-time dynamical systems using recurrence-based methods,” Chaos 20, 043130 (2010).
133. J. H. Feldhoff, R. V. Donner, J. F. Donges, N. Marwan, and J. Kurths, “ Geometric signature of complex synchronisation scenarios,” Europhys. Lett. 102, 30007 (2013).
134. J. F. Donges, R. V. Donner, K. Rehfeld, N. Marwan, M. H. Trauth, and J. Kurths, “ Identification of dynamical transitions in marine palaeoclimate records by recurrence network analysis,” Nonlinear Processes Geophys. 18, 545562 (2011).
135. J. Rockström, W. Steffen, K. Noone, A. Persson, F. S. Chapin III, E. F. Lambin, T. M. Lenton, M. Scheffer, C. Folke, H. J. Schellnhuber, B. Nykvist, C. A. de Wit, T. Hughes, S. van der Leeuw, H. Rodhe, S. Sorlin, P. K. Snyder, R. Costanza, U. Svedin, M. Falkenmark, L. Karlberg, R. W. Corell, V. J. Fabry, J. Hansen, B. Walker, D. Liverman, K. Richardson, P. Crutzen, and J. A. Foley, “ A safe operating space for humanity,” Nature 461, 472475 (2009).
136. J. F. Donges, R. V. Donner, M. H. Trauth, N. Marwan, H.-J. Schellnhuber, and J. Kurths, “ Nonlinear detection of paleoclimate-variability transitions possibly related to human evolution,” Proc. Natl. Acad. Sci. U.S.A. 108, 2042220427 (2011).
137. N. Marwan, M. H. Trauth, M. Vuille, and J. Kurths, “ Comparing modern and Pleistocene ENSO-like influences in NW Argentina using nonlinear time series analysis methods,” Clim. Dyn. 21, 317326 (2003).
138. T. D. Herbert, L. C. Peterson, K. T. Lawrence, and Z. Liu, “ Tropical ocean temperatures over the past 3.5 million years,” Science 328, 15301534 (2010).
139. D. J. Kennett, S. F. M. Breitenbach, V. V. Aquino, Y. Asmerom, J. Awe, J. U. L. Baldini, P. Bartlein, B. J. Culleton, C. Ebert, C. Jazwa, M. J. Macri, N. Marwan, V. Polyak, K. M. Prufer, H. E. Ridley, H. Sodemann, B. Winterhalder, and G. H. Haug, “ Development and disintegration of Maya political systems in response to climate change,” Science 338, 788791 (2012).
140. T. D. Herbert, “ Review of alkenone calibrations (culture, water column, and sediments),” Geochem. Geophys. Geosyst. 2, 2000GC000055, doi:10.1029/2000GC000055 (2001).
141. L. Li, Q. Li, J. Tian, P. Wang, H. Wang, and Z. Liu, “ A 4-Ma record of thermal evolution in the tropical western Pacific and its implications on climate change,” Earth Planet. Sci. Lett. 309, 1020 (2011).
142. M. B. Kennel, R. Brown, and H. D. I. Abarbanel, “ Determining embedding dimension for phase-space reconstruction using a geometrical construction,” Phys. Rev. A 45, 34033411 (1992).
143. G. H. Haug and R. Tiedemann, “ Effect of the formation of the Isthmus of Panama on Atlantic Ocean thermohaline circulation,” Nature 393, 673676 (1998).
144. M. Medina-Elizalde and D. W. Lea, “ The mid-Pleistocene transition in the tropical Pacific,” Science 310, 10091012 (2005).
145. Z. An, Y. Sun, W. Zhou, W. Liu, X. Qiang, X. Wang, F. Xian, P. Cheng, and G. S. Burr, “ Chinese loess and the East Asian Monsoon,” in Late Cenozoic Climate Change in Asia, Developments in Paleoenvironmental Research Vol. 16, edited by Z. An ( Springer Netherlands, Dordrecht, 2014), pp. 23143.
146. C. Karas, D. Nürnberg, A. K. Gupta, R. Tiedemann, K. Mohan, and T. Bickert, “ Mid-Pliocene climate change amplified by a switch in Indonesian subsurface throughflow,” Nat. Geosci. 2, 434438 (2009).
147. Y. Sun, Z. An, S. C. Clemens, J. Bloemendal, and J. Vandenberghe, “ Seven million years of wind and precipitation variability on the Chinese Loess plateau,” Earth Planet. Sci. Lett. 297, 525535 (2010).
148. B. Luque, L. Lacasa, F. Ballesteros, and J. Luque, “ Horizontal visibility graphs: Exact results for random time series,” Phys. Rev. E 80, 046103 (2009).
149. Y. Zou, J. Heitzig, R. V. Donner, J. F. Donges, J. D. Farmer, R. Meucci, S. Euzzor, N. Marwan, and J. Kurths, “ Power-laws in recurrence networks from dynamical systems,” Europhys. Lett. 98, 48001 (2012).
150. X.-H. Ni, Z.-Q. Jiang, and W.-X. Zhou, “ Degree distributions of the visibility graphs mapped from fractional Brownian motions and multifractal random walks,” Phys. Lett. A 373, 38223826 (2009).
151. L. Lacasa, A. Nuñez, E. Roldán, J. M. R. Parrondo, and B. Luque, “ Time series irreversibility: A visibility graph approach,” Eur. Phys. J. B 85, 217 (2012).
152. J. Theiler, S. Eubank, A. Longtin, B. Galdrikian, and J. D. Farmer, “ Testing for nonlinearity in time series: the method of surrogate data,” Physica D 58, 7794 (1992).
153. P. M. Grootes and M. Stuiver, “ Oxygen 18/16 variability in Greenland snow and ice with 10–3- to 105-year time resolution,” J. Geophys. Res. 102, 2645526470, doi:10.1029/97JC00880 (1997).
154. C.-F. Schleussner, D. Divine, J. F. Donges, A. Miettinen, and R. Donner, “ Indications for a North Atlantic ocean circulation regime shift at the onset of the Little Ice Age,” Clim. Dyn. (published online 2015).
155. T. Schreiber and A. Schmitz, “ Surrogate time series,” Physica D 142, 346382 (2000).
156. M. Thiel, M. C. Romano, J. Kurths, M. Rolfs, and R. Kliegl, “ Twin surrogates to test for complex synchronisation,” Europhys. Lett. 75, 535 (2006).
157. M. Paluš, D. Hartman, J. Hlinka, and M. Vejmelka, “ Discerning connectivity from dynamics in climate networks,” Nonlinear Processes Geophys. 18, 751763 (2011).

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We introduce the pyunicorn (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. pyunicorn is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics, or network surrogates. Additionally, pyunicorn provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis, recurrence networks, visibility graphs, and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology.


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