  Constructing networks from empirical time series data is often faced with the
as yet unsolved issue of how to avoid potentially superfluous network
constituents. Such constituents can result, e.g., from spatial and temporal
oversampling of the system's dynamics, and neglecting them can lead to severe
misinterpretations of network characteristics ranging from global to local
scale. We derive a perturbation-based method to identify potentially
superfluous network constituents that makes use of vertex and edge centrality
concepts. We investigate the suitability of our approach through analyses of
weighted small-world, scale-free, random, and complete networks.
