1 / 19

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.

caesar
Download Presentation

Vertex Edge Graphs

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related