VECTOR: A Framework to Identify and Quantify Structural Changes in Chromatin using Hi-C Data

Hi-C and related 3C technologies capture 3D genome architecture by measuring contact frequencies between genomic loci. These contact maps are often sparse and noisy, making comparison across samples challenging. Traditional metrics like Pearson correlation fail to capture their structural complexity. To address this, we present VECTOR (Von nEumann entropy deteCTiOn of stRuctural patterns), a novel framework that uses Von Neumann entropy and graph spectral theory to quantify chromatin organization from Hi-C data. By constructing normalized graph Laplacians from contact matrices, VECTOR captures both short- and long-range chromatin interactions, offering a robust, scale-invariant measure of 3D genome architecture. Applied to human and mouse datasets across diverse cell types, developmental stages, and replicates, VECTOR reveals reproducible entropy patterns that distinguish biological conditions, including cancer versus stem cells and early versus late embryonic stages. VECTOR outperforms existing Hi-C comparison tools such as ENT3C and HiCRep, especially in sparse or noisy datasets, by reliably differentiating biological replicates from non-biological ones. It further demonstrates stability across Hi-C resolutions and strides, and successfully detects genome-wide structural transitions linked to regulatory elements such as TADs and CTCF sites. When applied to sparse single-nucleus Hi-C data from mouse brain development, VECTOR accurately resolves developmental progression that is poorly captured by correlation-based methods. Our results establish VECTOR as a robust and interpretable tool for comparative Hi-C analysis, with broad applications in chromatin biology, development, and disease.