Line-Graph Node Centrality in Retrosynthesis

Abstract

Molecular structures are naturally represented as graphs in which nodes correspond to atoms and edges to bonds, enabling the application of graph-theoretical and linear algebraic tools to chemical problems. In retrosynthetic analysis, the central challenge is to identify strategic bonds whose disconnection simplifies a target molecule into accessible precursors. While computational approaches to synthesis planning have evolved from rule-based systems to artificial intelligence platforms, there remains a need for interpretable, quantitative, structure-based metrics that guide bond disconnection. In this work, we propose the use of line graphs of molecular graphs, in which nodes represent bonds of the original molecule, together with node centrality measures as a quantitative criterion for identifying strategic bonds. Because line graphs explicitly encode relationships between bonds, they provide a natural framework for retrosynthetic reasoning. We will first introduce the relevant graph-theoretical concepts and then demonstrate the approach in detail on six structurally diverse natural products: longifolene, hetisine-2,11,13-triol, auriculatol A, ineleganolide, quinocarcin, and papililone A. This is followed by a concise table of seven additional examples that highlights the bonds identified as most central and those chosen by chemists in the lab. In most cases, bonds identified as highly central correspond to key disconnections used in successful, and often shortest, syntheses, or suggest plausible alternative strategies. These results indicate that line-graph node centrality offers a simple, general, and chemically intuitive tool for guiding retrosynthetic analysis. To accompany this perspective and facilitate adoption of the metric, a web-based application has also been developed.