Topic 12 Graphs 1. Graphs Definition: Two types:

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Presentation transcript:

Topic 12 Graphs 1

Graphs Definition: Two types:

Undirected

Directed

Examples/Applications

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

Vacuum World (from AI) Source: centurion2.comcenturion2.com What belief states could we be in if we do a certain sequence of actions?

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

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

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

More Definitions Path: Length:

Cycle: Self-loop:

Incident edges

Simple graph: Acyclic graph:

Subgraph: Forest: Tree

Connected: Complete graph:

Weighted graph:

Graph Representations

Adjacency Matrix (undirected)

Adjacency Matrix (directed) Pros: Cons:

Adjaceny list (undirected)

Adjaceny list (directed)

Adjacency List Costs Space: Searching for edge between nodes: Adjacency check:

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

Breadth First Search

Implementing BFS

Depth-First Search

Recursive Algorithm

Iterative Algorithm