A Generative Model of Complex Networks Using Graphons and Neural Inverse Operators

2026-10-01

AI Summary

This study addresses the bottleneck wherein existing graph generative models struggle to simultaneously achieve mechanistic interpretability and generalization capability. To this end, it proposes a novel paradigm that unifies graph generation and parameter recovery within function space. Methodologically, the approach introduces multifractal-order Graphons to characterize complex topologies and designs neural inverse operators to enable cross-scale inference. By integrating the interpretability of mechanistic models with the amortized inference advantages of deep learning, this framework overcomes conventional training-scale limitations. Experimental results demonstrate that the proposed method achieves state-of-the-art zero-shot generative performance and supports network inference from single observations. Furthermore, in electroencephalography (EEG) case studies, the model exhibits sensitive tracking of dynamic brain state transitions, validating its practical utility in real-world neuroscientific applications.

Abstract

Generative graph models are central to understanding and simulating complex networks. However, existing approaches have complementary strengths and limitations. Mechanistic models offer interpretability but rely on instance-specific estimation methods. Deep generative models, on the other hand, offer amortized inference at the cost of interpretability and are largely limited to graph sizes seen during training. Scientific applications motivate a framework that retains the strengths of both paradigms. We bridge them by formulating both the generative model and parameter recovery in function space. A multifractal step graphon extends standard step graphons with a recursive construction that compactly parameterizes complex networks. This formulation admits a neural inverse operator to recover its parameters, enabling inference on unseen graph sizes. We evaluate our model, trained only on synthetic multifractal step graphon realizations, against both paradigms. Against a graph foundation model pretrained on empirical networks, our method achieves the best average performance on three of four metrics in a zero-shot graph-generation benchmark, indicating that the model transfers to real-world graphs. We also apply our method to single-observation networks, a regime largely inaccessible to deep models that require training corpora, where it performs comparably to an instance-specific method that optimizes on each graph. In a multi-subject EEG case study, the inferred parameters track a reversible change in brain state more sensitively than traditional network statistics. Together, these results indicate that mechanistic interpretability and amortized inference can be effectively unified in a generative graph model to enhance our understanding of complex networks.

Problem

• generative graph models
• complex networks
• mechanistic interpretability
• amortized inference
• graphons

Innovation

• Graphons
• Neural Inverse Operators
• Multifractal Step Graphon
• Amortized Inference
• Generative Graph Models