What question did this study set out to answer?

To investigate the dynamics of graph aggregation and the formation of hybrid discrete geometries through spectral methods.

March 24, 2026Open Access

Spectral Graph Coagulation and the Emergence of Hybrid Discrete Geometry

Key Points

To investigate the dynamics of graph aggregation and the formation of hybrid discrete geometries through spectral methods.
Introduced a model based on graph aggregation influenced by spectral compatibility.
Examined pairwise fusion events between discrete clusters using Laplacian-based metrics.
Analyzed resulting network characteristics including topology and spectral dimensions.
Identified an effective coagulation kernel, K(i,j) ~ (ij)^gamma with gamma ≈ 0.66.
Observed networks exhibit a large-scale spectral dimension close to three.
Generated sparse graph ensembles with extensive loop topology and persistent negative discrete curvature.

Abstract

We introduce a dynamical model of graph aggregation governed by spectral compatibility between discrete clusters. Connected graphs merge through pairwise fusion events whose acceptance depends on Laplacian-based observables, yet the resulting dynamics generates highly organized large-scale networks without any background geometry imposed a priori. The model produces an effective coagulation kernel K (i, j) ~ (ij) ᵍamma with gamma ≈ 0. 66, together with sparse graph ensembles exhibiting extensive loop topology, large-scale spectral dimension close to three, extended dominant eigenmodes, and persistent negative discrete curvature. Taken together, these results indicate the emergence of a hybrid discrete geometry: locally finite-dimensional, but globally non-Euclidean. Code, processed data, figures, and manuscript sources are archived separately in the associated Zenodo software/materials record.

Spectral Graph Coagulation and the Emergence of Hybrid Discrete Geometry

Key Points

Abstract

Cite This Study