Adaptive Cannistraci-Hebb Network Automata Modelling of Complex Networks for Path-based Link Prediction

Many complex networks have partially observed or evolving connectivity, making link prediction a fundamental task. Topological link prediction infers missing links using only network topology, with applications in social, biological, and technological systems. The Cannistraci-Hebb (CH) theory provides a topological formulation of Hebbian learning, grounded on two pillars: (1) the **minimization of external links** within local communities, and (2) the **path-based definition of local communities** that capture homophilic (similarity-driven) interactions via paths of length 2 and synergetic (diversity-driven) interactions via paths of length 3. Building on this, we introduce the Cannistraci-Hebb Adaptive (CHA) network automata, an adaptive learning machine that automatically selects the optimal CH rule and path length to model each network. CHA unifies theoretical interpretability and data-driven adaptivity, bridging physics-inspired network science and machine intelligence. Across 1,269 networks from 14 domains, CHA consistently surpasses state-of-the-art methods—including SPM, SBM, graph embedding methods, and message-passing graph neural networks—while revealing the mechanistic principles governing link formation. Our code is available at https://github.com/biomedical-cybernetics/Cannistraci_Hebb_network_automata.