Graph

Mathematically speaking, a graph is a pair (V, E) where:

If vertices a and b share an edge e, we define that they are adjacent.
 * 1) V is a set of vertices
 * 2) E is a set of edges on V

Vocabulary

 * 1) The degree of a vertex in an undirected graph is the number of edges associated with it.
 * 2) Two vertices are called adjacent if there is an edge between them.

According to Edge Types

 * Directed (E contains ordered pairs).
 * Undirected (E contains unordered pairs). Undirected graphs usually are drawn with straight lines between the vertices.

According to Labeling

 * Vertex-labeled
 * Edge-labeled

According to Connectiveness

 * Connected, when there is a path for any two distinct vertices.
 * Disconnected, when it isn't connected.

According to Edge Completeness

 * Complete, a graph in which each pair of its distinct vertices is connected by an edge.
 * Incomplete, when it isn't complete.

Graph Examples

 * 1) The Web (the webpages are the vertices and the hyperlinks are the edges).
 * 2) The Semantic Web (the things are the vertices and the named relationships among things are the edges).
 * 3) Social network (the people are the vertices and the friendships are the edges).
 * 4) The human nervous system.

Trivias

 * Vertices are also called nodes or points.