Vertex Edge Graphs. What is a vertex-edge graph? A collection of points, some of which are joined...
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Transcript of Vertex Edge Graphs. What is a vertex-edge graph? A collection of points, some of which are joined...
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