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:

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…

Summary  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