Molecular Directed, Bidirected, and Multidirected graphs

A directed graph (or digraph) consists of a finite vertex set 𝑉 and a set of ordered edges 𝐸 ⊆ 𝑉 × 𝑉, each edge (𝑢, 𝑣) indicating a one-way connection from 𝑢 (source) to 𝑣 (target). A bidirected graph is a generalization of an undirected graph where each edge is assigned a direction at each of its endpoints independently, allowing more expressive edge orientation. A multidirected graph is a structure with vertices and edges, where edges may repeat, sources and targets are assigned, and multiplicities recorded. A molecular graph models a molecule with atoms as vertices and bonds as edges, representing its structural connectivity. In this paper, we examine definitions such as molecular bidirected graphs and multidirected graphs. These are concepts that extend molecular graphs by incorporating directional information.