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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 = [ V , E ] , 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.


In the above graph, the set of vertices are V = { u , v , w , r , s } and the set of edges are E = { u v , u w , w r , v r , r s , v s } .

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 .



u 2
v 3
w 2
r 3
s 2