Abstract: In this contribution, we investigate a graph to signal mapping with the objective of analysing intricate structural properties of graphs with tools borrowed from signal processing. We successfully use a graph-based semi-supervised learning approach to map nodes of a graph to signal amplitudes such that the resulting time series is smooth and the procedure efficient and scalable. Theoretical analysis of this method reveals that it essentially amounts to a linear graph-shift-invariant filter with the a priori knowledge put into the training set as input. Further analysis shows that we can interpret this filter as a Wiener filter on graphs. We finally build upon this interpretation to improve our results.