Fig. 1. Three topological representations of the aspirin molecule.

(A) Chemical structure of aspirin. (B) to (D) Topological representations of aspirin structure: (B) graph; (C) simplicial complex; and (D) hypergraph. Mathematically, a graph is a simplicial complex with only vertices (0-simplexes) and edges (1-simplexes). The simplicial complex includes higher-dimensional simplexes, such as 2-simplexes (triangles in yellow) and 3-simplexes (tetrahedrons in blue). Hypergraph is a further generalization of the simplicial complex by replacing simplexes with hyperedges.