In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A "graph" in this context is made up of "vertices" or "nodes" and lines called edges that connect them. A graph may be undirected, meaning that there is no distinction between the two vertices associated with each edge, or its edges may be directed from one vertex to another; see graph (mathematics) for more detailed definitions and for other variations in the types of graph that are commonly considered. Graphs are one of the prime objects of study in discrete mathematics.

Summary:

• Introduction to graph theory
• Trees and forests
• Shortest paths algorithms
• Graph data structures
• Distance and connectivity
• Centrality and prestige
• Optimal graph traversals
• Graph coloring
• Network flows
• Algebraic graph theory
• Random graphs
• Asymptotic growth