Cluster evolution and extended cluster notions in adaptive (co-evolving) networks

Investigate the temporal evolution of clusters in adaptive (co-evolving) systems and ascertain whether the conventional notion of a cluster must be extended, for example to distinguish between structural network clusters and status network clusters.

Background

Adaptive or co-evolving networks exhibit feedback between node states and network structure, leading to nonlinear dynamics with multiple time scales. These characteristics complicate the identification and tracking of clusters over time.

The authors highlight the need to understand how clusters evolve under such feedback and whether standard cluster definitions suffice or must be extended to capture distinctions such as structural versus status-based clustering.

References

Questions on how clusters evolve in time and if the notion of a cluster needs to be extended (e.g., to structural network clusters and status network clusters), will be a topic of future research.

— Dynamical systems and complex networks: A Koopman operator perspective  (2405.08940 - Klus et al., 2024) in Section 5 (Conclusion)

CNWA is reported as a complementary method rather than a headline metric, since preserving cluster identity across generations is an open problem.

— Self-Replicating Neural Cellular Automata: Quantifying Emergent Phenotypic and Genotypic Diversity in an OpenEnded Substrate  (2609.19902 - Jain et al., 17 Sep 2026) in Section 3.2.2, Genotypic Diversity (CNWA)