Graph Theory
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 $G=\left[V,E\right]$ , where $V$ is a finite set of vertices or nodes and each element of $E$ is a subset of $V$ with exactly $2$ elements. Typically, a graph is depicted as a set of dots (the vertices) connected by lines (the edges).
The order of a graph is | $V$ | (the number of vertices). A graph's size is | $E$ | , the number of edges. The degree of a vertex is the number of edges that connect to it.
Example:
In the above graph, the set of vertices are $V=\left\{u,v,w,r,s\right\}$ and the set of edges are $E=\left\{uv,uw,wr,vr,rs,vs\right\}$ .
The order of the graph is $5$ . The size of the graph is $6$ .
The number of edges that connect with vertex $u$ is $2$ and therefore the degree of the vertex $u$ is $2$ .
Vertices |
Degree |
$u$ | 2 |
$v$ | 3 |
$w$ | 2 |
$r$ | 3 |
$s$ | 2 |