A graph is a mathematical structure giving of a set of vertexes (v1, v2, v3) and a group of edges (e1, e2, e3). An edge is a set of vertexes. The two vertexes are named the edge endpoints. They are used to model real-world machines such as a city road network or the Internet airline connections. The wireframe drawings in computer graphics are another part of graphs.

A graph may be either directed or undirected. Intuitively, an undirected edge models a "duplex" or "two-way" connection between its endpoints, while a directed edge is a one-way connection, and is typically shown as an arrow. A directed edge is often named an arc. Mathematically, an undirected edge is an unordered pair of end points, and an arc is an ordered pair. You may need, why not use a single undirected edge for a two-way street. It's usually simpler and less error-prone to stick with all undirected or all directed edges.

An undirected graph may have at most edges, while a directed graph may have at most   edges. A graph is called sparse if it has many lesser than this many edges, and intense if it has closer to   edges.