Jump to ContentJump to Main Navigation
Show Summary Details

Acta Geophysica

6 Issues per year


IMPACT FACTOR 2015: 0.945
5-year IMPACT FACTOR: 1.061

SCImago Journal Rank (SJR) 2015: 0.581
Source Normalized Impact per Paper (SNIP) 2015: 0.779
Impact per Publication (IPP) 2015: 0.937

Open Access
Online
ISSN
1895-7455
See all formats and pricing
Volume 60, Issue 3 (Jun 2012)

Issues

Visibility graph analysis of geophysical time series: Potentials and possible pitfalls

Reik Donner
  • Research Domain IV — Transdisciplinary Concepts & Methods, Potsdam Institute for Climate Impact Research, Potsdam, Germany
  • Email:
/ Jonathan Donges
  • Research Domain IV — Transdisciplinary Concepts & Methods, Potsdam Institute for Climate Impact Research, Potsdam, Germany
  • Department of Physics, Humboldt University of Berlin, Berlin, Germany
  • Email:
Published Online: 2012-04-28 | DOI: https://doi.org/10.2478/s11600-012-0032-x

Abstract

Recently, complex network approaches to time series analysis have been developed and successfully applied to geophysical records. In this paper, the visibility graph approach is re-considered, which has been found useful as an alternative tool for describing the fractal properties of a time series. The interpretation of various graph-theoretical measures in the context of visibility graphs, their mutual interdependence, and their sensitivity in the presence of missing values and uncertainties (posing typical challenges in geophysical time series analysis) are thoroughly discussed. The obtained results are illustrated for some exemplary records from different fields of geosciences.

Keywords: Geophysical time series; complex networks; fractals; uncertainty

  • [1] Abe, S., and N. Suzuki (2004), Scale-free network of earthquakes, Europhys. Lett. 65, 581–586, DOI: 10.1209/epl/i2003-10108-1. http://dx.doi.org/10.1209/epl/i2003-10108-1 [Crossref]

  • [2] Ahmadlou, M., H. Adeli, and A. Adeli (2010), New diagnostic EEG markers of the Alzheimer’s disease using visibility graphs, J. Neural Transm. 117, 1099–1109, DOI: 10.1007/s00702-010-0450-3. http://dx.doi.org/10.1007/s00702-010-0450-3 [Crossref]

  • [3] Albert, R., and A.-L. Barabasi (2002), Statistical mechanics of complex networks, Rev. Mod. Phys. 74, 47–97, DOI: 10.1103/RevModPhys.74.47. http://dx.doi.org/10.1103/RevModPhys.74.47 [Crossref]

  • [4] Albert, R., H. Jeong, and A.-L. Barabasi (2000), Error and attack tolerance of complex networks, Nature 406, 378–382, DOI: 10.1038/35019019. http://dx.doi.org/10.1038/35019019 [Crossref]

  • [5] Baiesi, M., and M. Paczuski (2004), Scale-free networks of earthquakes and aftershocks, Phys. Rev. E 69, 066106, DOI: 10.1103/PhysRevE.69.066106. http://dx.doi.org/10.1103/PhysRevE.69.066106 [Crossref]

  • [6] Barrat, A., and M. Weigt (2000), On the properties of small-world network models, Eur. Phys. J. B 13, 547–560, DOI: 10.1007/s100510050067. http://dx.doi.org/10.1007/s100510050067 [Crossref]

  • [7] Barthelemy, M. (2004), Betweenness centrality in large complex networks, Eur. Phys. J. B 38, 163–168, DOI:10.1140/epjb/e2004-00111-4. http://dx.doi.org/10.1140/epjb/e2004-00111-4 [Crossref]

  • [8] Bialonski, S., M.-T. Horstmann, and K. Lehnertz (2010), From brain to earth and climate systems: Small-world interaction networks or not?, Chaos 20, 013134, DOI: 10.1063/1.3360561. http://dx.doi.org/10.1063/1.3360561 [Crossref]

  • [9] Boccaletti, S., V. Latora, Y. Moreno, M. Chavez, and D.-U. Huang (2006), Complex networks: structure and dynamics, Phys. Rep. 424, 175–308, DOI: 10.1016/j.physrep.2005.10.009. http://dx.doi.org/10.1016/j.physrep.2005.10.009 [Crossref]

  • [10] Costa, L. da F., F.A. Rodrigues, G. Travieso, and P.R. Villas Boas (2007), Characterization of complex networks: a survey of measurements, Adv. Phys. 56, 167–242, DOI: 10.1080/00018730601170527. http://dx.doi.org/10.1080/00018730601170527 [Crossref]

  • [11] Davidsen, J., P. Grassberger, and M. Paczuski (2008), Networks of recurrent events, a theory of records, and an application to finding causal signatures in seismicity, Phys. Rev. E 77, 066104, DOI: 10.1103/PhysRevE.77.066104. http://dx.doi.org/10.1103/PhysRevE.77.066104 [Crossref]

  • [12] de Floriani, L., P. Marzano, and E. Puppo (1994), Line-of-sight communication on terrain models, Int. J. Geograph. Inform. Sci. 8, 329–342, DOI: 10.1080/02693799408902004. http://dx.doi.org/10.1080/02693799408902004 [Crossref]

  • [13] Dong, Z., and X. Li (2010), Comment on “Network analysis of human heartbeat dynamics” [Appl. Phys. Lett. 96, 073703 (2010)], Appl. Phys. Lett. 96, 266101, DOI: 10.1063/1.3458811. http://dx.doi.org/10.1063/1.3458811

  • [14] Donges, J.F., Y. Zou, N. Marwan, and J. Kurths (2009), The backbone of the climate network, Europhys. Lett. 87, 48007, DOI: 10.1209/0295-5075/87/48007. http://dx.doi.org/10.1209/0295-5075/87/48007 [Crossref]

  • [15] Donges, J.F., R.V. Donner, K. Rehfeld, N. Marwan, M.H. Trauth, and J. Kurths (2011a), Identification of dynamical transitions in marine palaeoclimate records by recurrence network analysis, Nonlin. Proc. Geophys. 18, 545–562, DOI: 10.5194/npg-18-545-2011. http://dx.doi.org/10.5194/npg-18-545-2011 [Crossref]

  • [16] Donges, J.F., R.V. Donner, M.H. Trauth, N. Marwan, H.J. Schellnhuber, and J. Kurths (2011b), Nonlinear detection of paleoclimate-variability transitions possibly related to human evolution, Proc. Natl. Acad. Sci. USA 108, 20422–20427, DOI: 10.1073/pnas.1117052108. http://dx.doi.org/10.1073/pnas.1117052108 [Crossref]

  • [17] Donner, R.V., Y. Zou, J.F. Donges, N. Marwan, and J. Kurths (2010), Recurrence networks — a novel paradigm for nonlinear time series analysis, New J. Phys. 12, 033025, DOI: 10.1088/1367-2630/12/3/033025. [Crossref]

  • [18] Donner, R.V., M. Small, J.F. Donges, N. Marwan, Y. Zou, R. Xiang, and J. Kurths (2011), Recurrence-based time series analysis by means of complex network methods, Int. J. Bifurcation Chaos 21, 1019–1048, DOI: 10.1142/S0218127411029021. http://dx.doi.org/10.1142/S0218127411029021 [Crossref]

  • [19] Dykoski, C.A., R.L. Edwards, H. Cheng, D. Yuan, Y. Cai, M. Zhang, Y. Lin, J. Qing, Z. An, and J. Revenaugh (2005), A high-resolution, absolute dated Holocene and deglacial Asian monsoon record from Dongge Cave, China, Earth Planet. Sci. Lett. 233, 71–86, DOI: 10.1016/j.epsl.2005.01.036. http://dx.doi.org/10.1016/j.epsl.2005.01.036 [Crossref]

  • [20] Elsner, J.B., T.H. Jagger, and E.A. Fogarty (2009), Visibility network of United States hurricanes, Geophys. Res. Lett. 36, L16702, DOI: 10.1029/2009GL039129. http://dx.doi.org/10.1029/2009GL039129 [Crossref]

  • [21] Gallos, L.K., C. Song, and H.A. Makse (2008), Scaling of degree correlations and its influence on diffusion in scale-free networks, Phys. Rev. Lett. 100, 248701, DOI: 10.1103/PhysRevLett.100.248701. http://dx.doi.org/10.1103/PhysRevLett.100.248701 [Crossref]

  • [22] Goh, K.-I., B. Kahng, and D. Kim (2001), Universal behavior of load distribution in scale-free networks, Phys. Rev. Lett. 87, 278701, DOI: 10.1103/PhysRevLett.87.278701. http://dx.doi.org/10.1103/PhysRevLett.87.278701 [Crossref]

  • [23] Gutin, G., T. Mansour, and S. Severini (2011), A characterization of horizontal visibility graphs and combinatorics on words, Physica A 390, 2421–2428, DOI: 10.1016/j.physa.2011.02.031. http://dx.doi.org/10.1016/j.physa.2011.02.031 [Crossref]

  • [24] Holme, P., B.J. Kim, C.N. Yoon, and S.K. Han (2002), Attack vulnerability of complex networks, Phys. Rev. E 65, 056109, DOI: 10.1103/PhyRevE.65.056109. http://dx.doi.org/10.1103/PhysRevE.65.056109 [Crossref]

  • [25] Jimenez, A., K.F. Tiampo, A.M. Posadas, F. Luzon, and R. Donner (2009), Analysis of complex networks associated to seismic clusters near the Itoiz reservoir dam, Eur. Phys. J. ST 174, 181–195, DOI: 10.1140/epjst/e2009-01099-1. [Crossref]

  • [26] Kitsak, M., S. Havlin, G. Paul, M. Riccaboni, F. Pammolli, and H.E. Stanley (2007), Betweenness centrality of fractal and nonfractal scale-free model networks and tests on real networks, Phys. Rev. E 75, 056115, DOI: 10.1103/PhysRevLett.87.278701. http://dx.doi.org/10.1103/PhysRevE.75.056115 [Crossref]

  • [27] Lacasa, L., and R. Toral (2010), Description of stochastic and chaotic series using visibility graphs, Phys. Rev. E 82, 036120, DOI: 10.1103/PhysRevE.82.036120. http://dx.doi.org/10.1103/PhysRevE.82.036120 [Crossref]

  • [28] Lacasa, L., B. Luque, F. Ballesteros, J. Luque, and J.C. Nuno (2008), From time series to complex networks: The visibility graph, Proc. Natl. Acad. Sci. USA 105, 4972–4975, DOI: 10.1073_pnas.0709247105.

  • [29] Lacasa, L., B. Luque, J. Luque, and J.C. Nuno (2009), The visibility graph: A new method for estimating the Hurst exponent of fractional Brownian motion, Europhys. Lett. 86, 30001, DOI: 10.1209/0295-5075/86/30001. http://dx.doi.org/10.1209/0295-5075/86/30001 [Crossref]

  • [30] Lacasa, L., A. Núñez, E. Roldán, J.M.R. Parrondo, and B. Luque (2011), Time series irreversibility: a visibility graph approach, arXiv:1108.1691v1 [physics. data-an].

  • [31] Liu, C., W.-X. Zhou, and W.-K. Yuan (2010), Statistical properties of visibility graph of energy dissipation rates in three-dimensional fully developed turbulence, Physica A 389, 2675–2681, DOI: 10.1016/j.physa.2010.02.043. http://dx.doi.org/10.1016/j.physa.2010.02.043 [Crossref]

  • [32] Lozano-Perez, T., and M.A. Wesley (1979), An algorithm for planning collision-free paths among polyhedral obstacles, Comm. ACM 22, 560–570, DOI: 10.1145/359156.359164. http://dx.doi.org/10.1145/359156.359164 [Crossref]

  • [33] Lukas, R., S.P. Hayes, and K. Wyrtki (1984), Equatorial sea level response during the 1982–1983 El Nino, J. Geophys. Res. 89,C6, 10425–10430, DOI: 10.1029/JC089iC06p10425. http://dx.doi.org/10.1029/JC089iC06p10425 [Crossref]

  • [34] Luque, B., L. Lacasa, F. Ballesteros, and J. Luque (2009), Horizontal visibility graphs: Exact results for random time series, Phys. Rev. E 80, 046103, DOI: 10.1103/PhysRevE.80.046103. http://dx.doi.org/10.1103/PhysRevE.80.046103 [Crossref]

  • [35] Luque, B., L. Lacasa, F.J. Ballesteros, and A. Robledo (2011), Feigenbaum graphs: A complex network perspective to chaos, PLoS One 6, e22411, DOI: 10.1371/journal.pone.0022411. http://dx.doi.org/10.1371/journal.pone.0022411 [Crossref]

  • [36] Luque, B., L. Lacasa, F.J. Ballesteros, and A. Robledo (2012), Analytical properties of horizontal visibility graphs in the Feigenbaum scenario, Chaos 22, 013109, DOI: 10.1063/1.3676686. http://dx.doi.org/10.1063/1.3676686 [Crossref]

  • [37] Nagy, G. (1994), Terrain visibility, Comp. Graph. 18, 763–773, DOI: 10.1016/0097-8493(94)90002-7. http://dx.doi.org/10.1016/0097-8493(94)90002-7 [Crossref]

  • [38] Newman, M. (2003), The structure and function of complex networks, SIAM Rev. 45, 167–256, DOI: 10.1137/S003614450342480. http://dx.doi.org/10.1137/S003614450342480 [Crossref]

  • [39] Ni, X.-H., Z.-Q. Jiang, and W.-X. Zhou (2009), Degree distributions of the visibility graphs mapped from fractional Brownian motions and multifractal random walks, Phys. Lett. A 373, 3822–3826, DOI: 10.1016/j.physleta.2009.08.041. http://dx.doi.org/10.1016/j.physleta.2009.08.041 [Crossref]

  • [40] Núñez, A., L. Lacasa, E. Valero, J.P. Gómez, and B. Luque (2011), Detecting series periodicity with horizontal visibility graphs, arXiv:1108.1693v1 [physics. data-an].

  • [41] Núñez, A.M., L. Lacasa, J.P. Gomez, and B. Luque (2012), Visibility algorithms: A short review. In: Y. Zhang (ed.), New Frontiers in Graph Theory, InTech, Rijeka, 119–152.

  • [42] Qian, M.-C., Z.-Q. Jiang, and W.-X. Zhou (2010), Universal and nonuniversal allometric scaling behaviors in the visibility graphs of world stock market indices, J. Phys. A 43, 335002, DOI: 10.1088/1751-8113/43/33/335002. http://dx.doi.org/10.1088/1751-8113/43/33/335002 [Crossref]

  • [43] Ravasz, E., and A.-L. Barabasi (2003), Hierarchical organization in complex networks, Phys. Rev. E 67, 026112, DOI:10.1103/PhysRevE.67.026112. http://dx.doi.org/10.1103/PhysRevE.67.026112 [Crossref]

  • [44] Santiago, A., J.P. Cardenas, J.C. Losada, R.M. Benito, A.M. Tarquis, and F. Borondo (2008), Multiscaling of porous soils as heterogeneous complex networks, Nonlin. Proc. Geophys. 15, 893–902, DOI: 10.5194/npg-15-893-2008. http://dx.doi.org/10.5194/npg-15-893-2008 [Crossref]

  • [45] Shao, Z.-G. (2010), Network analysis of human heartbeat dynamics, Appl. Phys. Lett. 96, 073703, DOI: 10.1063/1.3308505. http://dx.doi.org/10.1063/1.3308505 [Crossref]

  • [46] Song, C., S. Havlin, and H.A. Makse (2006), Origins of fractality in the growth of complex networks, Nature Phys. 2, 275–281, DOI: 10.1038/nphys266. http://dx.doi.org/10.1038/nphys266 [Crossref]

  • [47] Tang, Q., J. Liu, and H. Liu (2010), Comparison of different daily streamflow series in US and China, under a viewpoint of complex networks, Mod. Phys. Lett. B 24, 1541–1547, DOI: 10.1142/S0217984910023335. http://dx.doi.org/10.1142/S0217984910023335 [Crossref]

  • [48] Telesca, L., and M. Lovallo (2012), Analysis of seismic sequences by using the method of visibility graph, Europhys. Lett. 97, 50002, DOI: 10.1209/0295-5075/97/50002. http://dx.doi.org/10.1209/0295-5075/97/50002 [Crossref]

  • [49] Telford, R.J., E. Heegaard, and H.J.B. Birks (2004), All age-depth models are wrong: but how badly?, Quat. Sci. Rev. 23, 1–5, DOI: 10.1016/j.quascirev.2003.11.003. http://dx.doi.org/10.1016/j.quascirev.2003.11.003 [Crossref]

  • [50] Theiler, J. (1990), Estimating fractal dimensions, J. Opt. Soc. Am. A 7, 1055–1073, DOI: 10.1364/JOSAA.7.001055. http://dx.doi.org/10.1364/JOSAA.7.001055 [Crossref]

  • [51] Tsonis, A.A., and P.J. Roebber (2004), The architecture of the climate network, Physica A 333, 497–504, DOI: 10.1016/j.physa.2003.10.045. http://dx.doi.org/10.1016/j.physa.2003.10.045 [Crossref]

  • [52] Turner, A., M. Doxa, D. O’sullivan, and A. Penn (2001), From isovists to visibility graphs: A methodology for the analysis of architectural space, Env. Plann. B 28, 103–121, DOI: 10.1068/b2684. http://dx.doi.org/10.1068/b2684 [Crossref]

  • [53] Watts, D.J., and S.H. Strogatz (1998), Collective dynamics of ’small-world’ networks, Nature 393, 409–410, DOI: 10.1038/30918. http://dx.doi.org/10.1038/30918 [Crossref]

  • [54] Xie, W.-J., and W.-X. Zhou (2011), Horizontal visibility graphs transformed from fractional Brownian motions: Topological properties versus the Hurst index, Physica A 390, 3592–3601, DOI: 10.1016/j.physa.2011.04.020. http://dx.doi.org/10.1016/j.physa.2011.04.020 [Crossref]

  • [55] Yang, Y., J. Wang, H. Yang, and J. Mang (2009), Visibility graph approach to exchange rate series, Physica A 388, 4431–4437, DOI: 10.1016/j.physa.2009.07.016. http://dx.doi.org/10.1016/j.physa.2009.07.016 [Crossref]

  • [56] Zaliapin, I., E. Foufoula-Georgiou, and M. Ghil (2010), Transport on river networks: A dynamic tree approach, J. Geophys. Res. 115, F00A15, DOI: 10.1029/2009JF001281. http://dx.doi.org/10.1029/2009JF001281 [Crossref]

About the article

Published Online: 2012-04-28

Published in Print: 2012-06-01


Citation Information: Acta Geophysica, ISSN (Online) 1895-7455, ISSN (Print) 1895-6572, DOI: https://doi.org/10.2478/s11600-012-0032-x. Export Citation

© 2012 Institute of Geophysics, Polish Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Jonathan F. Donges, Jobst Heitzig, Boyan Beronov, Marc Wiedermann, Jakob Runge, Qing Yi Feng, Liubov Tupikina, Veronika Stolbova, Reik V. Donner, Norbert Marwan, Henk A. Dijkstra, and Jürgen Kurths
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2015, Volume 25, Number 11, Page 113101
[2]
Lucas Lacasa, Vincenzo Nicosia, and Vito Latora
Scientific Reports, 2015, Volume 5, Page 15508
[3]
Pouya Manshour, M Reza Rahimi Tabar, and Joachim Peinke
Journal of Statistical Mechanics: Theory and Experiment, 2015, Volume 2015, Number 8, Page P08031
[4]
Xin Lan, Hongming Mo, Shiyu Chen, Qi Liu, and Yong Deng
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2015, Volume 25, Number 8, Page 083105
[5]
Hongping Wang, Hongming Mo, Rehan Sadiq, Yong Hu, and Yong Deng
Computers & Industrial Engineering, 2015
[6]
C.-F. Schleussner, D. V. Divine, J. F. Donges, A. Miettinen, and R. V. Donner
Climate Dynamics, 2015
[7]
Jonathan D. Phillips, Wolfgang Schwanghart, and Tobias Heckmann
Earth-Science Reviews, 2015, Volume 143, Page 147
[8]
Jonathan F. Donges, Irina Petrova, Alexander Loew, Norbert Marwan, and Jürgen Kurths
Climate Dynamics, 2015
[9]
Soumi Chaki, Akhilesh K. Verma, Aurobinda Routray, William K. Mohanty, and Mamata Jenamani
Journal of Petroleum Science and Engineering, 2014, Volume 123, Page 155
[10]
Shiyu Chen, Yong Hu, Sankaran Mahadevan, and Yong Deng
Physica A: Statistical Mechanics and its Applications, 2014, Volume 403, Page 1
[11]
Yong Zou, Michael Small, Zonghua Liu, and Jürgen Kurths
New Journal of Physics, 2014, Volume 16, Number 1, Page 013051
[12]
Alexander Radebach, Reik V. Donner, Jakob Runge, Jonathan F. Donges, and Jürgen Kurths
Physical Review E, 2013, Volume 88, Number 5
[13]
Luciano Telesca, Michele Lovallo, Alejandro Ramirez-Rojas, and Leticia Flores-Marquez
Physica A: Statistical Mechanics and its Applications, 2013, Volume 392, Number 24, Page 6571
[14]
Ángel M. Núñez, Bartolo Luque, Lucas Lacasa, Jose Patricio Gómez, and Alberto Robledo
Physical Review E, 2013, Volume 87, Number 5
[15]
Jonathan F.Donges, Reik V. Donner, and Jürgen Kurths
EPL (Europhysics Letters), 2013, Volume 102, Number 1, Page 10004

Comments (0)

Please log in or register to comment.
Log in