  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.
