Gauge-Equivariant Fourier Operators for Modular Structure Discovery in Temporal Graphs
Keywords:
Temporal Graphs, Gauge Equivariance, Spectral Theory, Modular StructureAbstract
The analysis of temporal graphs presents a persistent challenge in the field of network science, primarily due to the intricate interplay between evolving topologies and dynamic node features. Traditional spectral graph theories often falter when applied to time-varying domains because they inherently rely on fixed global coordinate systems, leading to misinterpretations of structural changes. To circumvent these limitations, this paper introduces the concept of Gauge-Equivariant Fourier Operators, a novel theoretical framework designed specifically for modular structure discovery in continuous-time temporal graphs. By treating temporal graphs as discrete manifolds endowed with local gauge symmetries, we define an operator that preserves the structural and functional invariants of the network irrespective of the local coordinate choices made at individual nodes. This paper establishes the conceptual foundation of these operators, translates the principles of gauge theory into algorithmic network analysis, and details a comprehensive methodology for extracting dynamic communities. Furthermore, we provide extensive empirical validation across multiple dynamic network topologies, demonstrating that our proposed framework significantly outperforms contemporary temporal clustering techniques. The findings illuminate the profound advantages of incorporating geometric deep learning principles, specifically gauge equivariance, into the spectral domain, offering a robust tool for analyzing complex adaptive systems ranging from neurobiology to social dynamics.
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Copyright (c) 2026 Arlene Cornelius, Angela Clarence, Jieun Pyo
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