Vertex Edge Graphs

Vertex Edge

Graphs

What is a vertex-edge graph? A collection of points, some of which are

joined by line segments or curves

Examples:

Vertex A point on the graph.

Edge A line segment or curve connecting the

vertices of a graph.

In the Real-World Vertices may represent things such as

people or places. Edges may represent connections such

as roads or relationships.What are the

edges, and what do they

represent?

What about the vertices?

Complete Graph A graph in which every vertex is

adjacent to every other vertex.

Which of these is complete?

A B

Digraph A directed vertex edge graph

Degree of the Vertex The number of edges that enter a

vertex. What is the degree of vertex

A?

What is the degree of vertex

C?

2

4

Real World Example The vertex edge graph below represents

five people: Bob (B), Dustin (D), Mike (M), Sue (S) and Tammy (T).

An edge connecting two vertices indicates that those two people have a

class together.

Who has a class with Mike?

Tammy & Sue

Who does not have a class with Bob?

Tammy & Mike

Using Matrices to Represent a Vertex-Edge Graph

We can use an adjacency matrix to represent the vertex-edge graph. Step 1: Create a matrix listing all vertices

in the row and column. Step 2: Fill in the matrix listing the number

of relationships between the two points. If they share an edge, there will be a “1”If there is no relationship, there will be a

“0”

Create a Matrix using the following Vertex-Edge Graph:

Create a Matrix using the following Vertex-Edge Graph:

R

V

U

T

S

Drawing a Vertex-Edge Graph Use the following matrix to create the

vertex-edge graph that corresponds.

Drawing a Vertex-Edge Graph Use the following matrix to create the

vertex-edge graph that corresponds.

Extended Relationships A railway serves four cities: Harrisburg,

Baltimore, Philadelphia and Atlantic City. Trains travel between Harrisburg and Baltimore, Harrisburg and Philadelphia, and Philadelphia and Atlantic City.

Draw a vertex edge graph and it’s adjacency matrix to represent this situation.

Railway Continued… If we take , we can see the relationship

that is formed by using 2 trains.

What relationship would give?

Summary3-2-1 On a separate sheet of paper to turn in,

list: 3 vocabulary words you have learned and

their relationship to the vertex-edge graph

2 reasons to use a vertex-edge graph 1 real-world example of a vertex-edge

graph