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?
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?
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
S
V
T
U
Drawing a Vertex-Edge Graph
 Use
the following matrix to create the
vertex-edge graph that corresponds.
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
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…
we take 𝐴 2 , we can see the
relationship that is formed by using 2
trains.
 If
 What
relationship would 𝐴
3
give?
Summary
3-2-1
 On
list:



a separate sheet of paper to turn in,
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