We present a new cycle flow based method for finding fuzzy partitions of weighted directed networks coming from time series data. We show that this method overcomes essential problems of most existing clustering approaches, which tend to ignore important directional information by considering only one-step, one-directional node connections. Our method introduces a novel measure of communication between nodes using multi-step, bidirectional transitions encoded by a cycle decomposition of the probability flow. Symmetric properties of this measure enable us to construct an undirected graph that captures information flow of the original graph seen by the data and apply clustering methods designed for undirected graphs. Finally, we demonstrate our algorithm by analyzing earthquake time series data, which naturally induce (time-)directed networks. This article has been published originally in EPL, DOI: 10.1209/0295-5075/108/68008. This version differs from the published version by minor formatting details.