A library for algebraic construction and manipulation of edge-indexed graphs in Haskell. Based on the theory of algebraic edge graphs. The top-level module EdgeGraph defines the core data type EdgeGraph.EdgeGraph which is a deep embedding of six graph construction primitives EdgeGraph.empty, EdgeGraph.edge, EdgeGraph.overlay, EdgeGraph.into, EdgeGraph.pits and EdgeGraph.tips. More conventional graph representations can be found in EdgeGraph.AdjacencyMap and EdgeGraph.Incidence. The type classes defined in EdgeGraph.Class and EdgeGraph.HigherKinded.Class can be used for polymorphic graph construction and manipulation. Also see EdgeGraph.Fold that defines the Boehm-Berarducci encoding of algebraic edge graphs and provides additional flexibility for polymorphic graph manipulation. This is an experimental library and the API will be unstable until version 1.0.0.