Chordless cycle filtrations for dimensionality detection in complex networks via topological data analysis
This provides a method for revealing hidden geometry in networks like social or biological systems, which is incremental as it combines existing techniques in a novel way.
The paper tackles the problem of estimating the dimensionality of complex networks with underlying hyperbolic geometry by introducing a chordless cycle-based topological data analysis weighting scheme, achieving effective dimensionality detection through a neural network trained on synthetic graphs that transfers to real-world networks without retraining.
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 novel topological data analysis weighting scheme for graphs, based on chordless cycles, aimed at estimating the dimensionality of networks in a data-driven way. We further show that the resulting descriptors can effectively estimate network dimensionality using a neural network architecture trained in a synthetic graph database constructed for this purpose, which does not need 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.