Spectral Graph Entropy of Chromatin: A von Neumann Framework for Multiscale Polymer Organization from Hi-C

Hi-C contact maps encode multiscale chromatin folding, yet extracting quantitative and physically interpretable descriptors directly from these matrices remains challenging due to sparsity, depth variation, and the coexistence of loop-, domain-, and compartment-scale interactions. We introduce VECTOR, a graph-spectral framework that quantifies chromatin organization through the von Neumann entropy of the normalized contact-map Laplacian. By constructing distance-banded egographs for each genomic locus, VECTOR provides scale-resolved measures of configurational disorder spanning ∼10²-10⁷ bp. Short-range entropy systematically decreases at topological associating domain (TAD) boundaries, whereas long-range entropy captures compartmental reorganization. Entropy scaling reveals shallow exponents (α ≈ 0.04-0.06) and a monotonic compaction-disorder relation linking P(s) scaling to entropy deficits. Polymer simulations with tunable loop strength and A/B contrast confirm predictable spectral and entropic responses to physically meaningful perturbations. VECTOR is reproducible across replicates, robust to resolution and sequencing depth, and remains informative for sparse single-nucleus Hi-C, offering a compact, physics-grounded framework for multiscale chromatin architecture.