<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD Journal Publishing DTD v3.0 20080202//EN" "https://jats.nlm.nih.gov/nlm-dtd/publishing/3.0/journalpublishing3.dtd">
<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" article-type="research-article" dtd-version="3.0" xml:lang="en">
<front>
<journal-meta>
<journal-id journal-id-type="publisher">NPG</journal-id>
<journal-title-group>
<journal-title>Nonlinear Processes in Geophysics</journal-title>
<abbrev-journal-title abbrev-type="publisher">NPG</abbrev-journal-title>
<abbrev-journal-title abbrev-type="nlm-ta">Nonlin. Processes Geophys.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">1607-7946</issn>
<publisher><publisher-name>Copernicus Publications</publisher-name>
<publisher-loc>Göttingen, Germany</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.5194/npg-21-451-2014</article-id>
<title-group>
<article-title>Regional and inter-regional effects in evolving climate networks</article-title>
</title-group>
<contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Hlinka</surname>
<given-names>J.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Hartman</surname>
<given-names>D.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Jajcay</surname>
<given-names>N.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Vejmelka</surname>
<given-names>M.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Donner</surname>
<given-names>R.</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Marwan</surname>
<given-names>N.</given-names>
<ext-link>https://orcid.org/0000-0003-1437-7039</ext-link>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Kurths</surname>
<given-names>J.</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Paluš</surname>
<given-names>M.</given-names>
<ext-link>https://orcid.org/0000-0001-8474-1436</ext-link>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
</contrib-group><aff id="aff1">
<label>1</label>
<addr-line>Department of Nonlinear Dynamics and Complex Systems, Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vodarenskou vezi 2, 182 07 Prague 8, Czech Republic</addr-line>
</aff>
<aff id="aff2">
<label>2</label>
<addr-line>Potsdam Institute for Climate Impact Research (PIK), 14473 Potsdam, Germany</addr-line>
</aff>
<pub-date pub-type="epub">
<day>01</day>
<month>04</month>
<year>2014</year>
</pub-date>
<volume>21</volume>
<issue>2</issue>
<fpage>451</fpage>
<lpage>462</lpage>
<permissions>
<copyright-statement>Copyright: &#x000a9; 2014 J. Hlinka et al.</copyright-statement>
<copyright-year>2014</copyright-year>
<license license-type="open-access">
<license-p>This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit <ext-link ext-link-type="uri"  xlink:href="https://creativecommons.org/licenses/by/3.0/">https://creativecommons.org/licenses/by/3.0/</ext-link></license-p>
</license>
</permissions>
<self-uri xlink:href="https://npg.copernicus.org/articles/21/451/2014/npg-21-451-2014.html">This article is available from https://npg.copernicus.org/articles/21/451/2014/npg-21-451-2014.html</self-uri>
<self-uri xlink:href="https://npg.copernicus.org/articles/21/451/2014/npg-21-451-2014.pdf">The full text article is available as a PDF file from https://npg.copernicus.org/articles/21/451/2014/npg-21-451-2014.pdf</self-uri>
<abstract>
<p>Complicated systems composed of many interacting subsystems are frequently studied as complex
networks. In the simplest approach, a given real-world system is represented
by an undirected graph composed of nodes standing for the subsystems and
non-oriented unweighted edges for interactions present among the nodes; the
characteristic properties of the graph are subsequently studied and related
to the system&apos;s behaviour. More detailed graph models may include edge
weights, orientations or multiple types of links; potential time-dependency
of edges is conveniently captured in so-called evolving networks. Recently,
it has been shown that an evolving climate network can be used to disentangle
different types of El Niño episodes described in the literature. The time evolution of several graph
characteristics has been compared with the intervals of El Niño and La
Niña episodes. In this study we identify the sources of the evolving
network characteristics by considering a reduced-dimensionality description
of the climate system using network nodes given by rotated principal
component analysis. The time evolution of structures in local intra-component
networks is studied and compared to evolving inter-component connectivity.</p>
</abstract>
<counts><page-count count="12"/></counts>
</article-meta>
</front>
<body/>
<back>
<ref-list>
<title>References</title>
<ref id="ref1">
<label>1</label><mixed-citation publication-type="other" xlink:type="simple">Albert, R., Jeong, H., and Barabasi, A. L.: Internet – Diameter of the World Wide Web, Nature, 401, 130–131, 1999.</mixed-citation>
</ref>
<ref id="ref2">
<label>2</label><mixed-citation publication-type="other" xlink:type="simple">Arenas, A., Diaz-Guilera, A., Kurths, J., Moreno, Y., and Zhou, C.: Synchronization in complex networks, Phys. Reports, 469, 93–153, 2008.</mixed-citation>
</ref>
<ref id="ref3">
<label>3</label><mixed-citation publication-type="other" xlink:type="simple">Barabási, A.-L. and Albert, R.: Emergence of scaling in random network, Science, 286, 509–512, 1999.</mixed-citation>
</ref>
<ref id="ref4">
<label>4</label><mixed-citation publication-type="other" xlink:type="simple">Bialonski, S. and Lehnertz, K.: Assortative mixing in functional brain networks during epileptic seizures, Chaos, 23, 033139, &lt;a href=&quot;http://dx.doi.org/10.1063/1.4821915&quot;&gt;https://doi.org/10.1063/1.4821915&lt;/a&gt;, 2013.</mixed-citation>
</ref>
<ref id="ref5">
<label>5</label><mixed-citation publication-type="other" xlink:type="simple">Bialonski, S., Horstmann, M.-T., and Lehnertz, K.: From brain to earth and climate systems: Small-world interaction networks or not?, Chaos, 20, 013134, &lt;a href=&quot;http://dx.doi.org/10.1063/1.3360561&quot;&gt;https://doi.org/10.1063/1.3360561&lt;/a&gt;, 2010.</mixed-citation>
</ref>
<ref id="ref6">
<label>6</label><mixed-citation publication-type="other" xlink:type="simple">Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., and Hwang, D.-U.: Complex networks: Structure and dynamics, Phys. Reports, 424, 175–308, 2006.</mixed-citation>
</ref>
<ref id="ref7">
<label>7</label><mixed-citation publication-type="other" xlink:type="simple">Bullmore, E. and Sporns, O.: Complex brain networks: graph theoretical analysis of structural and functional systems, Nat. Rev. Neurosci., 10, 186–198, 2009.</mixed-citation>
</ref>
<ref id="ref8">
<label>8</label><mixed-citation publication-type="other" xlink:type="simple">Donges, J. F., Zou, Y., Marwan, N., and Kurths, J.: The backbone of the climate network, Europhys. Lett., 87, 48007, &lt;a href=&quot;http://dx.doi.org/10.1209/0295-5075/87/48007&quot;&gt;https://doi.org/10.1209/0295-5075/87/48007&lt;/a&gt;, 2009a.</mixed-citation>
</ref>
<ref id="ref9">
<label>9</label><mixed-citation publication-type="other" xlink:type="simple">Donges, J. F., Zou, Y., Marwan, N., and Kurths, J.: Complex networks in climate dynamics, Eur. Phys. J., 174, 157–179, 2009b.</mixed-citation>
</ref>
<ref id="ref10">
<label>10</label><mixed-citation publication-type="other" xlink:type="simple">Faloutsos, M., Faloutsos, P., and Faloutsos, C.: On power-law relationships of the internet topology, Comput. Commun. Rev., 29, 251–262, 1999.</mixed-citation>
</ref>
<ref id="ref11">
<label>11</label><mixed-citation publication-type="other" xlink:type="simple">Fountalis, I., Bracco, A., and Dovrolis, C.: Spatio-temporal network analysis for studying climate patterns, Clim. Dynam., 42, 879–899, &lt;a href=&quot;http://dx.doi.org/10.1007/s00382-013-1729-5&quot;&gt;https://doi.org/10.1007/s00382-013-1729-5&lt;/a&gt;, 2013.</mixed-citation>
</ref>
<ref id="ref12">
<label>12</label><mixed-citation publication-type="other" xlink:type="simple">Friston, K. J., Frith, C. D., Liddle, P. F., and Frackowiak, R. S. J.: Functional Connectivity – The Principal-Component Analysis Of Large (PET) Data Sets, J. Cereb. Blood Flow Metabol., 13, 5–14, 1993.</mixed-citation>
</ref>
<ref id="ref13">
<label>13</label><mixed-citation publication-type="other" xlink:type="simple">Groth, A. and Ghil, M.: Multivariate singular spectrum analysis and the road to phase synchronization. Phys. Rev. E, 84, 036206, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevE.84.036206&quot;&gt;https://doi.org/10.1103/PhysRevE.84.036206&lt;/a&gt;, 2011.</mixed-citation>
</ref>
<ref id="ref14">
<label>14</label><mixed-citation publication-type="other" xlink:type="simple">Guimera, R., Mossa, S., Turtschi, A., and Amaral, L. A. N.: The worldwide air transportation network: Anomalous centrality, community structure, and cities&apos; global roles, P. Natl. Acad. Sci. USA, 102, 7794–7799, 2005.</mixed-citation>
</ref>
<ref id="ref15">
<label>15</label><mixed-citation publication-type="other" xlink:type="simple">Hartman, D., Hlinka, J., Palus, M., Mantini, D., and Corbetta, M.: The role of nonlinearity in computing graph-theoretical properties of resting-state functional magnetic resonance imaging brain networks, Chaos, 21, 013119, &lt;a href=&quot;http://dx.doi.org/10.1063/1.3553181&quot;&gt;https://doi.org/10.1063/1.3553181&lt;/a&gt;, 2011.</mixed-citation>
</ref>
<ref id="ref16">
<label>16</label><mixed-citation publication-type="other" xlink:type="simple">Heikes, R. and Randall, D. A.: Numerical Integration of the Shallow-Water Equations on a Twisted Icosahedral Grid, Part I: Basic Design and Results of Tests, Mon. Weather Rev., 123, 1862–1880, 1995.</mixed-citation>
</ref>
<ref id="ref17">
<label>17</label><mixed-citation publication-type="other" xlink:type="simple">Heitzig, J., Donges, J. F., Zou, Y., Marwan, N., and Kurths, J.: Node-weighted measures for complex networks with spatially embedded, sampled, or differently sized nodes, Eur. Phys. J., 85, 1–22, &lt;a href=&quot;http://dx.doi.org/10.1140/epjb/e2011-20678-7&quot;&gt;https://doi.org/10.1140/epjb/e2011-20678-7&lt;/a&gt;, 2012.</mixed-citation>
</ref>
<ref id="ref18">
<label>18</label><mixed-citation publication-type="other" xlink:type="simple">Hlinka, J., Paluš, M., Vejmelka, M., Mantini, D., and Corbetta, M.: Functional connectivity in resting-state fMRI: Is linear correlation sufficient?, Neuroimage, 54, 2218–2225, 2011.</mixed-citation>
</ref>
<ref id="ref19">
<label>19</label><mixed-citation publication-type="other" xlink:type="simple">Hlinka, J., Hartman, D., and Paluš, M.: Small-world topology of functional connectivity in randomly connected dynamical systems, Chaos, 22, 033107, &lt;a href=&quot;http://dx.doi.org/10.1063/1.4732541&quot;&gt;https://doi.org/10.1063/1.4732541&lt;/a&gt;, 2012.</mixed-citation>
</ref>
<ref id="ref20">
<label>20</label><mixed-citation publication-type="other" xlink:type="simple">Hlinka, J., Hartman, D., Vejmelka, M., Novotná, D., and Paluš, M.: Non-linear dependence and teleconnections in climate data: sources, relevance, nonstationarity, Clim. Dynam., &lt;a href=&quot;http://dx.doi.org/10.1007/s00382-013-1780-2&quot;&gt;https://doi.org/10.1007/s00382-013-1780-2&lt;/a&gt;, in press, 2013a.</mixed-citation>
</ref>
<ref id="ref21">
<label>21</label><mixed-citation publication-type="other" xlink:type="simple">Hlinka, J., Hartman, D., Vejmelka, M., Runge, J., Marwan, N., Kurths, J., and Paluš, M.: Reliability of Inference of Directed Climate Networks Using Conditional Mutual Information, Entropy, 15, 2023–2045, 2013b.</mixed-citation>
</ref>
<ref id="ref22">
<label>22</label><mixed-citation publication-type="other" xlink:type="simple">Holme, P. and Saramäki J.: Temporal networks, Physics Reports, 519, 97–125, 2012.</mixed-citation>
</ref>
<ref id="ref23">
<label>23</label><mixed-citation publication-type="other" xlink:type="simple">Jeong, H., Mason, S. P., Barabasi, A. L., and Oltvai, Z. N.: Lethality and centrality in protein networks, Nature, 411, 41–42, 2001.</mixed-citation>
</ref>
<ref id="ref24">
<label>24</label><mixed-citation publication-type="other" xlink:type="simple">Jones, P. W.: A user&apos;s guide for SCRIP: A spherical coordinate remapping and interpolation package, Los Alamos National Laboratory, Los Alamos, USA, 1997.</mixed-citation>
</ref>
<ref id="ref25">
<label>25</label><mixed-citation publication-type="other" xlink:type="simple">Kalnay, E., Kanamitsu, M., Kistler, R., Collins, W., Deaven, D., Gandin, L., Iredell, M., Saha, S., White, G., Woollen, J., Zhu, Y., Chelliah, M., Ebisuzaki, W., Higgins, W., Janowiak, J., Mo, K. C., Ropelewski, C., Wang, J., Leetmaa, A., Reynolds, R., Jenne, R., and Joseph, D.: The NCEP/NCAR 40-year reanalysis project, B. Am. Meteorol. Soc., 77, 437–471, 1996.</mixed-citation>
</ref>
<ref id="ref26">
<label>26</label><mixed-citation publication-type="other" xlink:type="simple">Kuhnert, M.-T., Elger, C. E., and Lehnertz, K.: Long-term variability of global statistical properties of epileptic brain networks, Chaos, 20, 043126, &lt;a href=&quot;http://dx.doi.org/10.1063/1.3504998&quot;&gt;https://doi.org/10.1063/1.3504998&lt;/a&gt;, 2010.</mixed-citation>
</ref>
<ref id="ref27">
<label>27</label><mixed-citation publication-type="other" xlink:type="simple">Mantegna, R. N.: Hierarchical structure in financial markets, Eur. Phys. J. B, 11, 193–197, 1999.</mixed-citation>
</ref>
<ref id="ref28">
<label>28</label><mixed-citation publication-type="other" xlink:type="simple">Newman, M. E. J.: The structure of scientific collaboration networks, P. Natl. Acad. Sci. USA, 98, 404–409, 2001.</mixed-citation>
</ref>
<ref id="ref29">
<label>29</label><mixed-citation publication-type="other" xlink:type="simple">Newman, M. E. J.: The structure and function of complex networks, SIAM Rev., 45, 167–256, 2003.</mixed-citation>
</ref>
<ref id="ref30">
<label>30</label><mixed-citation publication-type="other" xlink:type="simple">Paluš, M., Hartman, D., Hlinka, J., and Vejmelka, M.: Discerning connectivity from dynamics in climate networks, Nonlin. Processes Geophys., 18, 751–763, &lt;a href=&quot;http://dx.doi.org/10.5194/npg-18-751-2011&quot;&gt;https://doi.org/10.5194/npg-18-751-2011&lt;/a&gt;, 2011.</mixed-citation>
</ref>
<ref id="ref31">
<label>31</label><mixed-citation publication-type="other" xlink:type="simple">Radebach, A., Donner, R. V., Runge, J., Donges, J. F., and Kurths, J.: Disentangling different types of El Niño episodes by evolving climate network analysis, Phys. Rev. E, 88, 052807, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevE.88.052807&quot;&gt;https://doi.org/10.1103/PhysRevE.88.052807&lt;/a&gt;, 2013.</mixed-citation>
</ref>
<ref id="ref32">
<label>32</label><mixed-citation publication-type="other" xlink:type="simple">Rosvall, M., Trusina, A., Minnhagen, P., and Sneppen, K.: Networks and cities: An information perspective, Phys. Rev. Lett., 94, 028701, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevLett.94.028701&quot;&gt;https://doi.org/10.1103/PhysRevLett.94.028701&lt;/a&gt;, 2005.</mixed-citation>
</ref>
<ref id="ref33">
<label>33</label><mixed-citation publication-type="other" xlink:type="simple">Shirer, W. R., Ryali, S., Rykhlevskaia, E., Menon, V., and Greicius, M. D.: Decoding Subject-Driven Cognitive States with Whole-Brain Connectivity Patterns, Cerebral Cortex, 22, 158–165, 2012.</mixed-citation>
</ref>
<ref id="ref34">
<label>34</label><mixed-citation publication-type="other" xlink:type="simple">Steinhaeuser, K., Ganguly, A. R., and Chawla, N. V.: Multivariate and multiscale dependence in the global climate system revealed through complex networks, Clim. Dynam., 39, 889–895, 2012.</mixed-citation>
</ref>
<ref id="ref35">
<label>35</label><mixed-citation publication-type="other" xlink:type="simple">Tsonis, A. A. and Roebber, P. J.: The architecture of the climate network, Physica A, 333, 497–504, 2004.</mixed-citation>
</ref>
<ref id="ref36">
<label>36</label><mixed-citation publication-type="other" xlink:type="simple">Tsonis, A. A. and Swanson, K. L.: Topology and predictability of El Nino and La Nina networks, Phys. Rev. Lett., 100, 228502, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevLett.100.228502&quot;&gt;https://doi.org/10.1103/PhysRevLett.100.228502&lt;/a&gt;, 2008.</mixed-citation>
</ref>
<ref id="ref37">
<label>37</label><mixed-citation publication-type="other" xlink:type="simple">Tsonis, A. A., Wang, G., Swanson, K. L., Rodrigues, F. A., and Costa, L. D. F.: Community structure and dynamics in climate networks, Clim. Dynam., 37, 933–940, 2011.</mixed-citation>
</ref>
<ref id="ref38">
<label>38</label><mixed-citation publication-type="other" xlink:type="simple">Vejmelka, M. and Paluš, M.: Partitioning Networks into Clusters and Residuals with Average Association, Chaos, 20, 033103, &lt;a href=&quot;http://dx.doi.org/10.1063/1.3460360&quot;&gt;https://doi.org/10.1063/1.3460360&lt;/a&gt;, 2010.</mixed-citation>
</ref>
<ref id="ref39">
<label>39</label><mixed-citation publication-type="other" xlink:type="simple">Vejmelka, M., Pokorná, L., Hlinka, J., Hartman, D., Jajcay, N., and Paluš, M.: Non-random correlation structures and dimensionality reduction of multivariate climate data, Clim. Dynam., in review, 2014.</mixed-citation>
</ref>
<ref id="ref40">
<label>40</label><mixed-citation publication-type="other" xlink:type="simple">Wasserman, S. and Faust, K.: Social Network Analysis, Cambridge University Press, 1994.</mixed-citation>
</ref>
<ref id="ref41">
<label>41</label><mixed-citation publication-type="other" xlink:type="simple">Watts, D. J. and Strogatz, S. H.: Collective dynamics of &quot;small-world&quot; networks, Nature, 393, 440–442, 1998.</mixed-citation>
</ref>
<ref id="ref42">
<label>42</label><mixed-citation publication-type="other" xlink:type="simple">Yamasaki, K., Gozolchiani, A., and Havlin, S.: Climate networks around the globe are significantly affected by El Nino, Phys. Rev. Lett., 100, 228501, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevLett.100.228501&quot;&gt;https://doi.org/10.1103/PhysRevLett.100.228501&lt;/a&gt;, 2008.</mixed-citation>
</ref>
</ref-list>
</back>
</article>