This preprint studies the large-scale organization emerging from a model of spectral graph coagulation, where graphs grow through the merging of smaller components guided by spectral observables. Using a radial decomposition from a barycentric center, we analyze structural, transport, and curvature observables across clusters of different sizes. Main results: Universal radial collapse of volume profiles, revealing an effective dimension deff≈3deff≈3; Smooth confining transport potentials with partial universality; Persistent negative Forman curvature and moderate Gromov hyperbolicity, consistent with non‑Euclidean metric features; Degree heterogeneity explains most of the observed curvature, yet higher‑order structural correlations remain beyond degree‑preserving null models. The work shows that well‑defined large‑scale scaling universality can arise purely from relational dynamics, without imposing any underlying geometry.This version is the original preprint submitted to Journal of Statistical Mechanics: Theory and Experiment (JSTAT). It is shared under a CC BY 4.0 license in accordance with IOP Publishing’s preprint policy.
Eduardo Gonzalez-Granda Fernandez (Fri,) studied this question.