A graph is a collection of points and lines connecting some (possibly empty) subset of them. The points of a graph are called graph vertices, "nodes" or simply "points." Similarly, the lines connecting the vertices of a graph are called graph edges, "arcs" or "lines."

A graph G can be defined as a pair (V,E), where V is a set of vertices, and E is a set of edges between the vertices E ⊆ {(u,v) | u, v ∈ V}.


Graphs are a mathematical structure that model sets of objects that may or may not be connected with members from sets of edges or links.

A graph can be described through two different sets of mathematical objects:

  • A set of vertices.
  • A set of edges that connect pairs of vertices.

Graphs can be either directed or undirected.

  • Directed graphs contain edges that "connect" only one way.
  • Undirected graphs contain only edges that automatically connect two vertices together in both directions.