ElastoGraph: An Open-Source Algorithmic Framework for the Topological Assessment of Molecular Stiffness Applied to Polysaccharide Networks

Abstract

The prediction of mechanical properties at the molecular scale relies on matrix-based approaches, such as the diagonalization of large Hessian matrices in elastic network models (ENMs) or molecular dynamics (MD) simulations. These methods exhibit O(N3) computational complexity and map molecular connectivity to macroscopic stiffness through numerical operations that do not explicitly resolve load-transmission pathways. Here, we present 2 ElastoGraph, an open-source Python framework that shifts the analytical focus from numerical prediction to the topological mapping of elastic paths—the specific routes through which mechanical force is transmitted between terminal vertices. The algorithm achieves three objectives: (i) it identifies and prunes mechanically irrelevant subgraphs (r = 0) via cut-vertex analysis, isolating the subset of elastic paths that contribute to load transmission; (ii) it hierarchically classifies these paths using a k–d subgraph ranking based on graph distance and vertex-connectivity, providing a prioritized map of topological targets for chemical functionalization; and (iii) it computes effective elastic constants for series-parallel architectures through recursive edge reductions in O(N) time, while establishing rigorous topological bounds for non-series-parallel networks. Applied to the load-bearing backbones of cellulose and β-chitin, the framework reveals that under uniform edge weights both polysaccharides are topologically isomorphic, yielding an identical effective stiffness. However, the integration of a chemical parameterization module breaks this degeneracy: assigning relative stiffness values of k = 1.0 to covalent bonds and k = 0.10 to hydrogen bonds in cellulose, versus k = 0.15 for hydrogen bonds in β-chitin, yields differentiated mechanical profiles (keff = 0.45 for cellulose and keff = 0.52 for β-chitin). The framework computes these results in less than 0.01 s, representing an approximate 50-fold speedup compared to standard Hessian inversion on comparable synthetic networks. This framework complements molecular dynamics simulations by providing an interpretable topological baseline that identifies which bonds are worth functionalizing to tune macroscopic stiffness. Quantitative validation against experimental nanomechanical data will be the subject of future work. Beyond polysaccharides, this topology-driven framework is extensible to protein domains, DNA nanostructures, metal–organic frameworks, and two-dimensional materials, providing an interpretable baseline for the rational design of mechanically tunable molecular 3 systems across structural biology, soft matter, and nanotechnology. The source code, documentation, and benchmark datasets are freely available at https://github.com/yeyrecanals/ElastoGraph