The Functional Graph Library (FGL) is a Haskell library providing an inductive approach to graph data structures and algorithms. It offers multiple graph implementations (Tree-based and PatriciaTree-based) with varying performance characteristics, along with a comprehensive suite of graph algorithms including BFS, DFS, shortest path, max flow, min span tree, articulation points, biconnected components, dominators, and transitive closure. The library features a modular architecture with clear separation between core graph type classes, basic operations, and specific query algorithms. It supports both pure functional and monadic (imperative-style) graph manipulation, with utilities for automatic node labeling and graph construction. The library is actively maintained with recent updates supporting modern GHC versions and includes a thorough test suite with QuickCheck properties.