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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.

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Vertex Edge Graphs

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  1. Vertex Edge Graphs

  2. What is a vertex-edge graph? • A collection of points, some of which are joined by line segments or curves • Examples:

  3. Vertex • A point on the graph.

  4. Edge • A line segment or curve connecting the vertices of a graph.

  5. 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?

  6. Complete Graph • A graph in which every vertex is adjacent to every other vertex. • Which of these is complete? A B

  7. Digraph • A directed vertex edge graph

  8. 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

  9. 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.

  10. Who has a class with Mike? Tammy & Sue

  11. Who does not have a class with Bob? Tammy & Mike

  12. 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”

  13. Create a Matrix using the following Vertex-Edge Graph:

  14. Create a Matrix using the following Vertex-Edge Graph: R S V T U

  15. Drawing a Vertex-Edge Graph • Use the following matrix to create the vertex-edge graph that corresponds.

  16. Drawing a Vertex-Edge Graph • Use the following matrix to create the vertex-edge graph that corresponds.

  17. 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.

  18. Railway Continued… • If we take , we can see the relationship that is formed by using 2 trains. • What relationship would give?

  19. 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

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