Flow stability for dynamic community detection

TL;DR

This paper introduces a novel method for detecting communities in temporal networks by analyzing the dynamics of processes that do not necessarily reach a steady state, capturing multiple dynamical scales.

Contribution

It presents a new approach that considers the temporal ordering of edges and does not require a stationary state, improving community detection in dynamic systems.

Findings

Method effectively identifies communities in synthetic and real-world temporal networks.

Uncovers multiple dynamical scales within complex systems.

Handles non-stationary dynamics without steady-state assumptions.

Abstract

Many systems exhibit complex temporal dynamics due to the presence of different processes taking place simultaneously. An important task in such systems is to extract a simplified view of their time-dependent network of interactions. Community detection in temporal networks usually relies on aggregation over time windows or consider sequences of different stationary epochs. For dynamics-based methods, attempts to generalize static-network methodologies also face the fundamental difficulty that a stationary state of the dynamics does not always exist. Here, we derive a method based on a dynamical process evolving on the temporal network. Our method allows dynamics that do not reach a steady state and uncovers two sets of communities for a given time interval that accounts for the ordering of edges in forward and backward time. We show that our method provides a natural way to disentangle the different dynamical scales present in a system with synthetic and real-world examples.