Quantify micro/meso/macro contributions in spectral graph distance measures

Determine the relative contributions of microscale (individual edges and node neighborhoods), mesoscale (communities, core–periphery, and mixing patterns among groups), and macroscale (global graph-level properties) structures to the similarity values produced by spectral graph distance measures on networks, such as those derived from eigenmodes of the combinatorial Laplacian; provide a principled decomposition or attribution that isolates how each of the three scales influences the computed similarity.

Background

The paper discusses that many existing graph similarity measures emphasize different structural scales (micro, meso, macro). Spectral distance measures are noted to reflect multiple scales simultaneously due to the presence of high and low frequency eigenmodes, but their interpretability is hindered by the localization tradeoff between graph and frequency space.

The authors highlight a specific unresolved issue: despite spectral measures’ ability to capture multi-scale information, it is unclear how much each scale contributes to the final similarity score. Addressing this uncertainty would improve interpretability and guide the choice and application of spectral methods in unsupervised settings.