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A van der Waals surface graph is the graph defined on a van der Waals surface by the intersections of the atomic van der Waals spheres. A van der Waals shape graph has a vertex for each atom with a visible face on the van der Waals surface, and edges between vertices representing atoms with adjacent faces on the van der Waals surface. These are discrete invariants of three‐dimensional molecular shape. Some basic properties of van der Waals surface graphs are studied, including their relationship with the Voronoi diagram of the atom centres, and a class of molecular embeddings is identified for which the dual of the van der Waals surface graph coincides with the van der Waals shape graph.