1PIK Potsdam Institute of Climate Impact Research, P.O. Box 601203, 14412 Potsdam, Germany
2Department of Physics, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany
3Alfred-Wegener-Institut, Helmholtz-Zentrum für Polar- und Meeresforschung, Telegrafenberg A43, 14473 Potsdam, Germany
Received: 17 Dec 2013 – Revised: 27 Mar 2014 – Accepted: 05 May 2014 – Published: 25 Jun 2014
Abstract. Complex network theory has been successfully applied to understand the structural and functional topology of many dynamical systems from nature, society and technology. Many properties of these systems change over time, and, consequently, networks reconstructed from them will, too. However, although static and temporally changing networks have been studied extensively, methods to quantify their robustness as they evolve in time are lacking. In this paper we develop a theory to investigate how networks are changing within time based on the quantitative analysis of dissimilarities in the network structure.
Our main result is the common component evolution function (CCEF) which characterizes network development over time. To test our approach we apply it to several model systems, Erdős–Rényi networks, analytically derived flow-based networks, and transient simulations from the START model for which we control the change of single parameters over time. Then we construct annual climate networks from NCEP/NCAR reanalysis data for the Asian monsoon domain for the time period of 1970–2011 CE and use the CCEF to characterize the temporal evolution in this region. While this real-world CCEF displays a high degree of network persistence over large time lags, there are distinct time periods when common links break down. This phasing of these events coincides with years of strong El Niño/Southern Oscillation phenomena, confirming previous studies. The proposed method can be applied for any type of evolving network where the link but not the node set is changing, and may be particularly useful to characterize nonstationary evolving systems using complex networks.
Tupikina, L., Rehfeld, K., Molkenthin, N., Stolbova, V., Marwan, N., and Kurths, J.: Characterizing the evolution of climate networks, Nonlin. Processes Geophys., 21, 705-711, doi:10.5194/npg-21-705-2014, 2014.