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Graph Theory Fundamentals: Vertexes, Edges, and Graph Implementations

Explore the basics of graphs in Computer Science, understanding vertexes and edges, along with various graph implementations like adjacency lists and matrices. Learn traversal techniques such as depth-first and breadth-first traversal to navigate graphs effectively.

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Graph Theory Fundamentals: Vertexes, Edges, and Graph Implementations

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  1. CS112 Lab 11, April 15, 2010http://cs-people.bu.edu/deht/cs112_spring11/lab11/ Diane H. Theriault deht@cs.bu.edu http://cs-people.bu.edu/deht/

  2. Graphs • You can’t throw a rock in Computer Science without hitting a graph • Vertexes: the things in the graph • Edges: the relationships/connectivity between things. • G = (V,E) (Graph = (Vertexes, Edges))

  3. Graph Implementations • Adjacency lists • Each node has a list of other nodes it is connected to. • (alternatives) • Adjacency matrix • Edge List

  4. Constructing a Graph (Implementation) • (Go through code on p. 432 for reading in a graph from a file.) • http://algs4.cs.princeton.edu/41undirected/Graph.java.html

  5. Traversals • Most of the interesting things about graphs are tied up in how the nodes are connected to each other • Techniques for walking through graphs: • Depth-first traversal • Breadth-first traversal

  6. Depth-First Traversal • (p. 437) • Stack-based (recursive) • (Example) • http://algs4.cs.princeton.edu/41undirected/DepthFirstSearch.java.html

  7. Breadth-First Traversal • (p. 446) • Queue-based • (Example) • http://algs4.cs.princeton.edu/41undirected/BreadthFirstPaths.java.html

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