Adaptive rewiring: Connection density and emergent structure

Coupled oscillators evolve complex network connectivity structures as they rewire based on their ongoing dynamic synchronization. We investigated how connection density modulates this evolution, examining regimes ranging from sparse to full network connectivity. Systematic variation in connection density induced several transitions during network evolution. Below a threshold of 7%–8% connectivity, networks failed to develop clustered connections. Above this threshold, networks abruptly transitioned into a stable regime, in which they converged onto modular small-world topologies organized into communities of predictable number and size. At specific intermediate densities, networks formed “canonical structures”, i.e. densely connected modules that are evenly partitioned across nodes. Around a 30%–40% mid-density region, network evolution exhibited delayed convergence and metastability, suggesting transitions between competing configurations. As density increased further, modularity collapsed, hubs centralized, and networks became unstable. These results clarify the conditions under which modularity, hub structure, and rich-club organization emerge – or fail to emerge – in adaptive networks. • Adaptive rewiring networks exhibit distinct structural regimes as connection density increases. • A fine-grained density sweep reveals predictable transitions between sparse, modular, and collapsed states. • Probabilistic community inference identifies canonical modular configurations and their stability ranges. • Structural convergence criteria quantify stability and expose a narrow metastable density range. • Results clarify how local rewiring rules generate global organization and robustness patterns.