Molecular MultiGraph and Molecular Iterative MultiGraph

A multigraph permits multiple edges between the same pair of vertices, allowing the modeling of repeated or parallel relationships in networks and systems. An iterative multigraph is obtained by repeatedly applying multigraph transformations, generating a sequence of graphs that capture evolving multi-edge connectivity patterns. A molecular graph represents the structure of a chemical compound, where vertices correspond to atoms and edges represent chemical bonds. A molecular multigraph extends this concept by allowing multiple bonds (edges) between the same pair of atoms (vertices). Since research on iterative multigraphs is still in its early stages, applications in chemistry and related domains remain largely unexplored. In this paper, we present the formal definition of the Molecular Iterative-MultiGraph.