What are graphs?
 

When mathematicians talk about graph theory, they like to call the graphs - networks. A network consists of dots (are called vertices or nodes) and lines (are called edges or arcs). In a network, each arc has two verticies as the endpoints.

Here are some examples of networks:
 
  
 

We use graphs to illustrate and analyze relationships between different objects.   The edges of a graph express the relationships among the vertices.
 

Lets look at the degree of the vertex and graph.