The Fibonacci resilient network: Emergent resilience from a deterministic generative rule

Designing networks that balance information transfer efficiency with failure resilience remains a central challenge in critical infrastructure development. We present the Fibonacci Resilient Network (FRN), a generative framework employing multi-scalar connectivity patterns based on the Fibonacci sequence to create inherently decentralized, hub-free topologies. The framework offers three algorithms tailored for different deployment needs: Basic FRN (maximum performance), Fixed-Edge FRN (resource constraints), and Auto-Optimized FRN (goal-driven synthesis). Nodes connect at Fibonacci-derived intervals with controlled randomness, systematically embedding both local clustering and global shortcuts while avoiding the vulnerable hub structures of scale-free networks. Comprehensive comparative evaluation against classical models (Erdős-Rényi, Watts-Strogatz, Newman-Watts, Barabási-Albert, Kleinberg) on 2000-node networks reveals significant advantages. Under severe selective attacks (50 % node removal), FRN variants demonstrate exceptional resilience, maintaining network efficiency of 0.24 – 0.33 while preserving full connectivity. In contrast, classical models suffer catastrophic failure, either fragmenting into disconnected components or collapsing functionally. The Basic FRN demonstrates exceptional performance with average path length of 2.686 and algebraic connectivity of 8.172. Statistical analysis shows FRN generates approximately normal degree distributions rather than power-law structures, explaining its superior attack tolerance. The Auto-Optimized variant achieves target performance using 76 % fewer edges than dense configurations, demonstrating practical utility for infrastructure applications ranging from communication systems to transportation grids.