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Exploring Graphs: Definitions, Types, and Applications

Learn about graph theory, including definitions like paths and cycles, types such as directed and undirected graphs, and applications like transportation networks and social networks. Discover representation methods, search algorithms like BFS and DFS, and more. Join us in this fascinating journey through the world of graphs!

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Exploring Graphs: Definitions, Types, and Applications

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  1. Topic 12 Graphs 1

  2. Graphs • Definition: • Two types:

  3. Undirected

  4. Directed

  5. Examples/Applications

  6. Transportation Networks Shortest path? Source: pages.cs.wisc.edu

  7. Vacuum World (from AI) What belief states could we be in if we do a certain sequence of actions? Source: centurion2.com

  8. Social Network Are you an introvert? Who are you most friendly with? Source: infosthetics.com

  9. Graphical Models (from machine learning) What was the most likely sequence of weather given the actions (walking, shopping, cleaning) on those days? Source: wikipedia.org

  10. Graphical Models What is the most probable configuration that created this image? Source: PRML by Christopher Bishop

  11. More Definitions • Path: • Length:

  12. Cycle: • Self-loop:

  13. Incident edges

  14. Simple graph: • Acyclic graph:

  15. Subgraph: • Forest: • Tree

  16. Connected: • Complete graph:

  17. Weighted graph:

  18. Announcements • Homework 6 due • Test on Thursday (material up to Tuesday) • Reminder: survey • Review on Wednesday

  19. Announcements • Survey • Quizzes/Graph sample problems online • Participation

  20. Graph Representations

  21. Adjacency Matrix (undirected)

  22. Storing for Undirected

  23. Adjacency Matrix (directed) Pros: Cons:

  24. Adjacency Matrix Costs • Space: • Adjacency check: • Listing edges of node:

  25. Adjacency list (undirected)

  26. Adjacency list (directed)

  27. Adjacency List Costs • Space: • Adjacency check: • Listing edges of node:

  28. Graph Search/Traversals • How do get from one node to another? • Why?

  29. Idea • Layers:

  30. Breadth First Search: Algorithm

  31. Example

  32. BFS Tree

  33. Depth-First Search • Applications: • Running time:

  34. Recursive Algorithm

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