AI RESEARCH
Departure from Regularity: Degree Heterogeneity and Eigengap as the Structural Drivers of ASE-LSE Latent Subspace Disagreement
arXiv CS.LG
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ArXi:2605.22346v1 Announce Type: cross Two of the most widely used methods for analysing graph data, Adjacency Spectral Embedding and Laplacian Spectral Embedding, often produce different results when applied to the same network. Yet the structural reasons behind this disagreement remain incompletely understood. This paper provides a structural account. We show that regularity is a sufficient condition for perfect agreement: when every node has the same number of connections, the two methods produce identical latent subspaces. Any departure from this regularity.