TL;DR
The findings illustrate that geometric insights grounded in hyperbolic geometry can offer powerful tools for understanding, embedding, and visualizing complex graph structures.
It is proved that ( 𝑑 + 1 ) -dimensional random dot product graphs generalize 𝑑 -dimensional random ball graphs up to constant factors and vice versa.
This work compares ball-and weighted graphs and gives a complete comparison in the one-dimensional case, and shows that the minimal dimension for ball graphs can at most be one larger than the minimal dimension for weighted graphs (weighted dimension), but also that the weighted dimension can exceed the ball dimension...
Graph machine learning tailored to planar graphs is developed, with an emphasis on the mathematical intuition that connects the topology of a plane embedding to the spectral and combinatorial structure ex- ploited by learning algorithms.
This approach demonstrates that models trained on small-scale random graphs learn to extract universal distance-preserving features, achieving robust generalization to large-scale, real-world networks that match or exceed the fidelity of classical, exact landmark-based embeddings.
This study introduces a fast lossless graph compression algorithm based on modern hyperbolic embedders that beats state-of-the-art by up to 42% on real-world graphs.
This work introduces a principled extension of Ollivier's Ricci curvature to complex-weighted graphs, which encompasses directed graphs as a special case and establishes fundamental theoretical properties of this new notion, including relations to the magnetic Laplacian and combinatorial upper and lower bounds that rel...
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