Skip to main content
SpringerLink
Log in

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

  • Research Article
  • Published:
Acta Geophysica Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Albert, R., and A.-L. Barabasi (2002), Statistical mechanics of complex networks, Rev. Mod. Phys. 74, 47–97, DOI: 10.1103/RevModPhys.74.47.

    Article  Google Scholar 

  • Albert, R., H. Jeong, and A.-L. Barabasi (2000), Error and attack tolerance of complex networks, Nature 406, 378–382, DOI: 10.1038/35019019.

    Article  Google Scholar 

  • Baiesi, M., and M. Paczuski (2004), Scale-free networks of earthquakes and aftershocks, Phys. Rev. E 69, 066106, DOI: 10.1103/PhysRevE.69.066106.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Barthelemy, M. (2004), Betweenness centrality in large complex networks, Eur. Phys. J. B 38, 163–168, DOI:10.1140/epjb/e2004-00111-4.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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].

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Nagy, G. (1994), Terrain visibility, Comp. Graph. 18, 763–773, DOI: 10.1016/0097-8493(94)90002-7.

    Article  Google Scholar 

  • Newman, M. (2003), The structure and function of complex networks, SIAM Rev. 45, 167–256, DOI: 10.1137/S003614450342480.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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].

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Ravasz, E., and A.-L. Barabasi (2003), Hierarchical organization in complex networks, Phys. Rev. E 67, 026112, DOI:10.1103/PhysRevE.67.026112.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Shao, Z.-G. (2010), Network analysis of human heartbeat dynamics, Appl. Phys. Lett. 96, 073703, DOI: 10.1063/1.3308505.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Theiler, J. (1990), Estimating fractal dimensions, J. Opt. Soc. Am. A 7, 1055–1073, DOI: 10.1364/JOSAA.7.001055.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Watts, D.J., and S.H. Strogatz (1998), Collective dynamics of ’small-world’ networks, Nature 393, 409–410, DOI: 10.1038/30918.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Domain IV — Transdisciplinary Concepts & Methods, Potsdam Institute for Climate Impact Research, Potsdam, Germany

    Reik V. Donner & Jonathan F. Donges

  2. Department of Physics, Humboldt University of Berlin, Berlin, Germany

    Jonathan F. Donges

Authors
  1. Reik V. Donner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jonathan F. Donges
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Reik V. Donner.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Donner, R.V., Donges, J.F. Visibility graph analysis of geophysical time series: Potentials and possible pitfalls. Acta Geophys. 60, 589–623 (2012). https://doi.org/10.2478/s11600-012-0032-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.2478/s11600-012-0032-x

Key words

Search

Navigation