  Understanding the dynamics of spatially extended systems represents a
challenge in diverse scientific disciplines, ranging from physics and
mathematics to the earth and climate sciences or the neurosciences. This
challenge has stimulated the development of sophisticated data analysis
approaches adopting concepts from network theory: systems are considered to be
composed of subsystems (nodes) which interact with each other (represented by
edges). In many studies, such complex networks of interactions have been
derived from empirical time series for various spatially extended systems and
have been repeatedly reported to possess the same, possibly desirable,
properties (e.g. small-world characteristics and assortativity). In this thesis
we study whether and how interaction networks are influenced by the analysis
methodology, i.e. by the way how empirical data is acquired (the spatial and
temporal sampling of the dynamics) and how nodes and edges are derived from
multivariate time series. Our modeling and numerical studies are complemented
by field data analyses of brain activities that unfold on various spatial and
temporal scales. We demonstrate that indications of small-world characteristics
and assortativity can already be expected due solely to the analysis
methodology, irrespective of the actual interaction structure of the system. We
develop and discuss strategies to distinguish the properties of interaction
networks related to the dynamics from those spuriously induced by the analysis
methodology. We show how these strategies can help to avoid misinterpretations
when investigating the dynamics of spatially extended systems.
