Journal : Acta Geophysica
Article : Visibility graph analysis of geophysical time series: Potentials and possible pitfalls

Authors :
Vallianatos, F.
Technological Educational Institute of Crete, Laboratory of Geophysics and Seismology, Crete, Greece,,
Tsallis, C.
Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems, Rio de Janeiro, Brazil,,
Sotolongo-Costa, O.
Catedra de Sistemas Complejos “Henri Poincare”, Universidad de La Habana,,
Celikoglu, A.
Department of Physics, Faculty of Science, Ege University, Izmir, Turkey,,
Abe, S.
Department of Physical Engineering, Mie University, Mie, Japan,,
Bunde, A.
Institut fur Theoretische Physik, Giessen, Germany,,
Donner, R.
Research Domain IV – Transdisciplinary Concepts & Methods, Potsdam Institute for Climate Impact Research, Potsdam, Germany,,
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,
Publishing house : Instytut Geofizyki PAN
Publication date : 2012
Number : Vol. 60, no. 3
Page : 589 – 623

: Abe, S., and N. Suzuki (2004), Scale-free network of earthquakes, Europhys. Lett. 65, 581-586, DOI: 10.1209/epl/i2003-10108-1.
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.
Albert, R., and A.-L. Barabasi (2002), Statistical mechanics of complex networks, Rev. Mod. Phys. 74, 47-97, DOI: 10.1103/RevModPhys.74.47.
Albert, R., H. Jeong, and A.-L. Barabasi (2000), Error and attack tolerance of complex networks, Nature 406, 378-382, DOI: 10.1038/35019019.
Baiesi, M., and M. Paczuski (2004), Scale-free networks of earthquakes and aftershocks, Phys. Rev. E 69, 066106, DOI: 10.1103/PhysRevE.69.066106.
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.
Barthelemy, M. (2004), Betweenness centrality in large complex networks, Eur. Phys. J. B 38, 163-168, DOI:10.1140/epjb/e2004-00111-4.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Lacasa, L., A. Núñez, E. Roldán, J.M.R. Parrondo, and B. Luque (2011), Time series irreversibility: a visibility graph approach, arXiv:1108.1691v1
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.
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.
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.
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.
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.
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.
Nagy, G. (1994), Terrain visibility, Comp. Graph. 18, 763-773, DOI: 10.1016/0097-8493(94)90002-7.
Newman, M. (2003), The structure and function of complex networks, SIAM Rev. 45, 167-256, DOI: 10.1137/S003614450342480.
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.
Núñez, A., L. Lacasa, E. Valero, J.P. Gómez, and B. Luque (2011), Detecting series periodicity with horizontal visibility graphs, arXiv:1108.1693v1
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.
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.
Ravasz, E., and A.-L. Barabasi (2003), Hierarchical organization in complex networks, Phys. Rev. E 67, 026112, DOI:10.1103/PhysRevE.67.026112.
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.
Shao, Z.-G. (2010), Network analysis of human heartbeat dynamics, Appl. Phys. Lett. 96, 073703, DOI: 10.1063/1.3308505.
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.
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.
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.
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.
Theiler, J. (1990), Estimating fractal dimensions, J. Opt. Soc. Am. A 7, 1055-1073, DOI: 10.1364/JOSAA.7.001055.
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.
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.
Watts, D.J., and S.H. Strogatz (1998), Collective dynamics of ‘small-world’ networks, Nature 393, 409-410, DOI: 10.1038/30918.
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.
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.
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.
Qute : Vallianatos, F. ,Tsallis, C. ,Sotolongo-Costa, O. ,Celikoglu, A. ,Abe, S. ,Bunde, A. ,Donner, R. ,Donner, R. , Visibility graph analysis of geophysical time series: Potentials and possible pitfalls. Acta Geophysica Vol. 60, no. 3/2012