Deterministic Frequency--Domain Inference of Network Topology and Hidden Components via Structure--Behavior Scaling

2025-09-24

AI Summary

This work addresses the challenge of inferring hidden nodes and nonlinear interactions in complex systems from partial behavioral observations. We propose the first deterministic frequency-domain network reconstruction framework based on the Discrete Fourier Transform (DFT). Leveraging a cross-scale linear relationship between spectral intensity and node degree observed in evolutionary game dynamics, our method analyzes the frequency-domain characteristics of node payoff time series to simultaneously localize hidden nodes, estimate an upper bound on their number, and reconstruct the full network topology—without requiring prior structural knowledge. Our key contribution is the discovery and formal modeling of an analytically tractable linear mapping between network structure and behavioral dynamics in the frequency domain, combined with selective perturbation and spectral intensity analysis for robust inference. Extensive experiments on synthetic and real-world networks demonstrate significant improvements over state-of-the-art methods, with strong robustness, high computational efficiency, and excellent scalability to large-scale complex systems.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Game Theory and Economic Paradigms: Behavioral Game Theory

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Social Networks and Social Media: Computational social science

Abstract

Hidden interactions and components in complex systems-ranging from covert actors in terrorist networks to unobserved brain regions and molecular regulators-often manifest only through indirect behavioral signals. Inferring the underlying network structure from such partial observations remains a fundamental challenge, particularly under nonlinear dynamics. We uncover a robust linear relationship between the spectral strength of a node's behavioral time series under evolutionary game dynamics and its structural degree, $S propto k$, a structural-behavioral scaling that holds across network types and scales, revealing a universal correspondence between local connectivity and dynamic energy. Leveraging this insight, we develop a deterministic, frequency-domain inference framework based on the discrete Fourier transform (DFT) that reconstructs network topology directly from payoff sequences-without prior knowledge of the network or internal node strategies-by selectively perturbing node dynamics. The framework simultaneously localizes individual hidden nodes or identifies all edges connected to multiple hidden nodes, and estimates tight bounds on the number of hidden nodes. Extensive experiments on synthetic and real-world networks demonstrate that our method consistently outperforms state-of-the-art baselines in both topology reconstruction and hidden component detection. Moreover, it scales efficiently to large networks, offering robustness to stochastic fluctuations and overcoming the size limitations of existing techniques. Our work establishes a principled connection between local dynamic observables and global structural inference, enabling accurate topology recovery in complex systems with hidden elements.

Problem

• Inferring network structure from partial observations of behavioral signals
• Reconstructing network topology directly from node payoff sequences
• Localizing hidden nodes and estimating their number in complex systems

Innovation

• Leverages structural-behavioral scaling between node degree and spectral strength
• Uses deterministic frequency-domain inference based on discrete Fourier transform
• Reconstructs topology from payoff sequences by selectively perturbing node dynamics