The paper presents a minimalistic and elegant approach to working with graphs in Haskell. It is built on a rigorous mathematical foundation — an algebra of graphs — that allows us to apply equational reasoning for proving the correctness of graph transformation algorithms. Algebraic graphs let us avoid partial functions typically caused by `malformed graphs’ that contain an edge referring to a non-existent vertex. This helps to liberate APIs of existing graph libraries from partial functions.

The algebra of graphs can represent directed, undirected, reflexive and transitive graphs, as well as hypergraphs, by appropriately choosing the set of underlying axioms. The flexibility of the approach is demonstrated by developing a library for construction and transformation of polymorphic graphs.