# Flow stability for dynamic community detection

arXiv: https://arxiv.org/abs/2101.06131 · HTML: https://mlsanity.com/paper/2101.06131/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jan 2021.

## Built on by (most cited first, 8 of 8)

- [Longitudinal Modularity, a Modularity for Link Streams](https://mlsanity.com/paper/2408.16877/) (2024)
- [Redefining Event Types and Group Evolution in Temporal Data](https://mlsanity.com/paper/2403.06771/) (2024)
- [MCbiF: Measuring Topological Autocorrelation in Multiscale Clusterings via 2-Parameter Persistent Homology](https://mlsanity.com/paper/2510.14710/) (2025)
- [Bayesian Detection of Mesoscale Structures in Pathway Data on Graphs](https://mlsanity.com/paper/2301.11120/) (2023)
- [The Spectral Barycentre of a Set of Graphs with Community Structure](https://mlsanity.com/paper/2502.00038/) (2025)
- [Discovering Communities in Continuous-Time Temporal Networks by Optimizing L-Modularity](https://mlsanity.com/paper/2510.00741/) (2025)
- [Conditional Entropy of Heat Diffusion on Temporal Networks](https://mlsanity.com/paper/2605.21514/) (2026)
- [ComNetX: Local Hierarchical Adaptation for Dynamic Community Detection](https://mlsanity.com/paper/2608.16906/) (2026)

## Abstract (arXiv)

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.