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Graphs

Graphs. Ed. 2. and 3.: Chapter 12 Ed. 4.: Chapter 13. Graphs Graph ADT - What is a graph? - Graph methods Data structure for graphs - Edge list structure, adjacency list structure, adjacency matrix Graph Traversal - Depth-first search - Breadth-first search Directed graphs.

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Graphs

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  1. Graphs • Ed. 2. and 3.: Chapter 12 • Ed. 4.: Chapter 13

  2. Graphs • Graph ADT • - What is a graph? • - Graph methods • Data structure for graphs • - Edge list structure, adjacency list • structure, adjacency matrix • Graph Traversal • - Depth-first search • - Breadth-first search • Directed graphs

  3. The Graph Abstract Data Type

  4. (u, v) u v (Toronto) (Winnipeg) (v, u)

  5. u v (New York) (Winnipeg) (v, u)

  6. self-loop

  7. Graph Methods

  8. Data Structure Exercises 20.1

  9. Data Structure for Graphs

  10. element c1 c2 rank c3

  11. Edge Objects The edge object for an edge e storing element o has data fields for A reference to o · A Boolean indicator of whether e is directed or not · · References to the vertex objects in V associated with the endpoint vertices of e (if the edge e is undir ected) or to the origin and destination vertices of e (if the edge e is directed) · A reference to the position of the edge - object in container E Note: The last data field is the rank of the edge object in the container E if E is a vector.

  12. element With an edge list, some methods (edge - based) are fast while others need some efforts. For example, methods endVertices(), origin(), and destination() are fast because we can access edges directly. end vertex 1 or 0 end vertex

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