In this chapter, the term graph will mean a simple graph, that is, a graph without multiple edges or loops. Both directed and undirected graphs are permitted, although only a limited number of operations are currently implemented for digraphs. Subsequent versions of Magma will support weighted graphs and graphs with coloured edges and/or vertices.

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

A set system on a set S is a sequence of subsets of elements of S.