A nice graph theory book with examples written for SageMath by *David Joyner, Minh Van Nguyen, David Phillips*.
The book is under the following license http://www.gnu.org/copyleft/fdl.html.

http://world.mathigon.org/resources/Graph_Theory/graph.png

**Graph theory is fundamental in many fields.** 
You do not need to understand everything of it, you need to know which tool exists and where/when to use it.


# Table of content:

    Introduction to graph theory
        Graphs and digraphs
        Subgraphs and other graph types
        Representing graphs in a computer
        Graph transformation
        Isomorphic graphs
        New graphs from old
    Trees and forests
        Properties of trees
        Minimum spanning trees
        Binary trees
        Huffman codes
        Tree traversals
    Shortest paths algorithms
        Distance labels
        Searching graphs
        Bellman-Ford algorithm
        Dijkstra's algorithm
        Topological sort
        All-pairs shortest paths
    Graph data structures
        Priority queues
        Binary heaps
        Binomial heaps
        Binary search trees
    Distance and connectivity
        Path and distance
        Vertex and edge connectivity
        Menger’s theorem
        Network reliability
    Centrality and prestige
        Vertex centrality
        Edge centrality
        Ranking web pages
        Hub and authority
    Optimal graph traversals
        Eulerian graphs
        Hamiltonian graphs
        Chinese postman problem
        Traveling salesman problem
    Graph coloring
        Vertex coloring
        Edge coloring
        Chromatic polynomial
        Assignment and scheduling
    Maximum flow problems
        Flows and cuts
        Ford-Fulkerson theorem
        Edmonds-Karp algorithm
        Goldberg-Tarjan algorithm
        Path-flow decomposition
        Maximum weight closure
    Algebraic graph theory
        Laplacian and adjacency matrices
        Eigenvalues and eigenvectors
        Algebraic connectivity
        Graph invariants
        Cycle and cut spaces
    Random networks
        Network statistics
        Binomial random networks
        Erdos-Renyi networks
        Small-world networks
        Scale-free networks


# Follows the link down below of the lastest revision:
https://storage.googleapis.com/google-code-archive-downloads/v2/code.google.com/graphbook/latest-r1991.pdf

# Comment

There is some additional materials for this book here: https://bitbucket.org/mvngu/graphbook-supplement

**SageMath** (http://www.sagemath.org/index.html) seems to be an interesting project:
*SageMath is a free open-source mathematics software system licensed under the GPL. It builds on top of many existing open-source packages: NumPy, SciPy, matplotlib, Sympy, Maxima, GAP, FLINT, R and many more. Access their combined power through a common, Python-based language or directly via interfaces or wrappers.
Mission: Creating a viable free open source alternative to Magma, Maple, Mathematica and Matlab.*