  Eigen techniques such as empirical orthogonal function (EOF) or coupled
pattern (CP) / maximum covariance analysis have been frequently used for
detecting patterns in multivariate climatological data sets. Recently,
statistical methods originating from the theory of complex networks have been
employed for the very same purpose of spatio-temporal analysis. This climate
network (CN) analysis is usually based on the same set of similarity matrices
as is used in classical EOF or CP analysis, e.g., the correlation matrix of a
single climatological field or the cross-correlation matrix between two
distinct climatological fields. In this study, formal relationships as well as
conceptual differences between both eigen and network approaches are derived
and illustrated using exemplary global precipitation, evaporation and surface
air temperature data sets. These results allow to pinpoint that CN analysis can
complement classical eigen techniques and provides additional information on
the higher-order structure of statistical interrelationships in climatological
data. Hence, CNs are a valuable supplement to the statistical toolbox of the
climatologist, particularly for making sense out of very large data sets such
as those generated by satellite observations and climate model intercomparison
exercises.
