Both directed and undirected graphs are supported by Magma. In the case of undirected graphs, neither multiple edges nor loops are permitted. In the case of directed graphs, loops are permitted but multiple edges are disallowed. Both directed and undirected graphs may have vertex labellings and/or edge labellings.

Given a graph G, unless otherwise stated, the vertex set of G will be written as V or V(G) if it might be ambiguous, while the edge set of G will be written as E or E(G). We shall frequently use the term (p, q) graph to refer to a graph having p vertices and q edges.