Cycle-flow–based module detection in directed recurrence networks

¹ Institut für Mathematik und Informatik, Freie Universität Berlin - 14195 Berlin, Germany
² Zuse Institute Berlin - 14195 Berlin, Germany

Received: 31 July 2014
Accepted: 9 December 2014

Abstract

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 the 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.