In the branch of mathematics called graph theory, some words have different definitions.
In graph theory, a graph is a set of objects called vertices (or nodes) connected by links called edges . (It's not the same kind of graph you draw when you graph a function on coordinate axes.)
This kind of graph is sometimes also called a network .
A finite simple graph is an ordered pair , where is a finite set of vertices or nodes and each element of is a subset of with exactly elements. Typically, a graph is depicted as a set of dots (the vertices) connected by lines (the edges).
The order of a graph is | | (the number of vertices). A graph's size is | | , the number of edges. The degree of a vertex is the number of edges that connect to it.
In the above graph, the set of vertices are and the set of edges are .
The order of the graph is . The size of the graph is .
The number of edges that connect with vertex is and therefore the degree of the vertex is .