NeurIPS 2025

Adaptive Cannistraci-Hebb Network Automata
Modelling of Complex Networks for Path-based Link
Prediction
Jialin Zhao1,2
Alessandro Muscoloni1,3,4
Umberto Michieli5,6
Yingtao Zhang1,2
Carlo Vittorio Cannistraci1,2,3,4 ∗
1Center for Complex Network Intelligence (CCNI) †
2Dept. of Computer Science & Technology, 3School of Biomedical Engineering, Tsinghua University
4Biomedical Cybernetics Group, Technische Universität Dresden, Germany ‡
5University of Padova, Italy, 6Canva Research
Abstract
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 princi-
ples governing link formation. Our code is available at https://github.com/
biomedical-cybernetics/Cannistraci_Hebb_network_automata.
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Introduction
Many complex networks have a connectivity that might be only partially detected or that tends to grow
over time, hence the prediction of non-observed links is a...