Structural Description of Two-Dimensional Nanoscale Networks Using Graph Theory and Graph Growth Algorithms
Year: 2026
Type: preprint
Abstract: Nanostructured networks stand out among other nanostructures for their unique combinations of properties and easily scalable energy-efficient synthesis. Their structural organization is, however, difficult to describe using traditional approaches based on crystallinity. Although revealing distinct structural patterns, the nanoscale networks also have a substantial degree of randomness. Two-dimensional (2D) nanostructured networks self-assembled from nanoparticles present a unique opportunity to develop the methodology for structural description of such materials. We describe nanostructured networks as sets of nodes and edges with corresponding weights taking advantage of the mathematical apparatus of Graph Theory (GT). Being extracted from electron microscopy images, the GT descriptors readily identify nanoscale networks obtained under different chemical conditions. Also important is that among the prior studies the GT description of properties has been extensively discussed, while better understanding of adequate GT descriptors is lagging. All GT descriptors were found to be scale-dependent, with average nodal degree, centrality metrics, multi-fractal dimension, and Ollivier-Ricci curvature following smooth superlinear or sublinear trajectories over several thousands of nodes. Statistical analysis of topological and metric parameters of nodes and edges enables development of topometric graph growth algorithms (TOGGA) that capture the structural uniqueness of each nanoscale network. Similarly to the infinite tiling of unit cells in crystals, TOGGA models enabled the extrapolation of nanoscale network structure, commensurate with both micro- and macroscale samples over 10 million nodes and 20 million edges. The predictions of electric transport through the networks comparable in size to experimental samples enable identification of knowledge gaps for rapid design of conductive nanoscale networks. TOGGA models can be used to map out experimentally realistic structures for inverse design of nanoscale networks.
Source: ChemRxiv
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221117474