A GNU-FDL book on algorithmic graph theory by David Joyner, Minh Van Nguyen, and Nathann Cohen. This is an introductory book on algorithmic graph theory. Theory and algorithms are illustrated using the Sage open source mathematics software. To get an overview of the book, you can view the table of contents as shown below or download the complete book. This book is more commonly known as the "DaMN" book if you notice the first letter of the first name of each author. So feel free to call it the DaMN book :-)

A companion book is Explorations in Algebraic Graph Theory with Sage. This book covers how to use techniques from algebra to analyze many types of graphs.

The book is a work in progress; it is by no means complete yet. We as the authors work on it during our spare time. If you want to help out by contributing materials, that would be awesome and greatly appreciated.

The latest revision of the book is called latest-rxxx.

1. Introduction to graph theory
1. Graphs and digraphs
2. Subgraphs and other graph types
3. Representing graphs as matrices
4. Isomorphic graphs
5. New graphs from old
6. Common applications
7. Application: finite automata
2. Graph algorithms
1. Representing graphs in a computer
2. Graph searching
3. Weights and distances
4. Dijkstra's algorithm
5. Bellman-Ford algorithm
6. Floyd-Roy-Warshall algorithm
7. Johnson's algorithm
3. Trees and forests
1. Definitions and examples
2. Properties of trees
3. Minimum spanning trees
4. Binary trees
5. Huffman codes
6. Tree traversals
4. Tree data structures
1. Priority queues
2. Binary heaps
3. Binomial heaps
4. Binary search trees
5. AVL trees
5. Distance and connectivity
1. Paths and distance
2. Vertex and edge connectivity
3. Ford-Fulkerson theorem
4. Menger’s Theorem
5. Whitney’s Theorem
6. Centrality of a vertex
7. Network reliability
6. Optimal graph traversals
1. Eulerian graphs
2. Hamiltonian graphs
3. The Chinese Postman Problem
4. The Traveling Salesman Problem
7. Planar graphs
1. Planarity and Euler's Formula
2. Kuratowski's Theorem
3. Planarity algorithms
4. Graph Coloring
5. Vertex coloring
6. Edge coloring
7. Applications of graph coloring
8. Network flows
1. Flows and cuts
2. Ford and Fulkerson's theorem
3. Edmonds and Karp's algorithm
4. Goldberg and Tarjan's algorithm
9. Random graphs
1. Network statistics
2. Binomial random graph model
3. Erdos-Renyi model
4. Small-world networks
5. Scale-free networks
10. Graph problems and their LP formulations
1. Maximum average degree
2. Traveling Salesman Problem
3. Edge-disjoint spanning trees
4. Steiner tree
5. Linear arboricity
6. Acyclic edge coloring
7. H-minor