用无弦环分析网络拓扑，自动推断其隐含维度。
Chordless cycle filtrations for dimensionality detection in complex networks via topological data analysis
- 基于无弦环构建拓扑过滤，捕捉网络深层结构
- 在合成数据上训练的模型可直接用于真实网络
- 适合研究社交、生物等复杂网络的几何特性
从社交到生物系统，许多复杂网络表现出符合潜在双曲几何的结构模式。揭示该隐藏空间的维度，有助于解析社区结构、提升网络导航效率，并影响整体连通性与系统行为。本文提出一种基于无弦环的图拓扑数据分析加权方案，实现数据驱动的网络维度估计。通过在专为本研究构建的合成图数据库上训练神经网络，所得描述符可无需重新训练即有效迁移至真实网络。结合环感知过滤、代数拓扑与机器学习，该方法为揭示复杂网络的隐藏几何结构提供了鲁棒有效的手段，助力精准建模与低维嵌入。
原文摘要 · Abstract (English)
Many complex networks, ranging from social to biological systems, exhibit structural patterns consistent with an underlying hyperbolic geometry. Revealing the dimensionality of this latent space can disentangle the structural complexity of communities, impact efficient network navigation, and fundamentally shape connectivity and system behavior. We introduce a topological data analysis weighting scheme for graphs based on chordless cycles to estimate network dimensionality in a data-driven way. We further show that the resulting descriptors can effectively estimate network dimensionality using a neural network architecture trained on a synthetic graph database constructed for this purpose, which requires no retraining to transfer effectively to real-world networks. Thus, by combining cycle-aware filtrations, algebraic topology, and machine learning, our approach provides a robust and effective method for uncovering the hidden geometry of complex networks and guiding accurate modeling and low-dimensional embedding.
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