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lecture_10_graph_-_3in1_with_notes

# lecture_10_graph_-_3in1_with_notes - Graphs Outline What is...

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Graphs 2 Outline b What is a graph? b Graph’s applications b Terminology b Graph’s implementation b Breadth first search b Depth first search b Topological sort 3 Readings b Textbook s [Carrano] ch13

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4 Linked list 1 parent 1 child 5 Tree 1 parent multiple children 6 Directed graph vertex (node) edge 1 parent 1 child multiple parents multiple children A graph consists of a set of vertices and a set of edges between the vertices. In a tree, there is a unique path between any two nodes. In a graph, there may be more than one path between two nodes.
7 Example: travel planning shopping mall direct route 5 cost 8 Weighted directed graph 5 3 -2 5 1 0 In a weighted graph, edges have a weight (or cost) associated with it. Not all weights are labeled in this slides for simplicity. 9 Undirected graph edges are bidirectional In an undirected graph, edges are bidirectional.

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10 Complete graph •every pair of vertices has an edge between them •The number of edges : n(n-1)/2 = O(n 2 ) A graph is complete if every pair of vertices has an edge between them. The number of edges in a complete graph is n(n-1)/2, where n is the number of vertices. (Why is it so?). Therefore, the number of edges is O(n 2 ). A complete graph is also called a clique. 11 Path a c d e b A path between two vertices is a sequence of edges that begin at one vertex and end at another. The length of a path p is the number of edges in p. A simple path never visits the same vertex more than once. A path between two vertices is a sequence of edges that begin at one vertex and end at another. The length of a path p is the number of edges in p. A simple path never visits the same vertex more than once. 12 Cycle a c g d e b f A cycle is a path that begins and ends at the same vertex. Simple cycle is a simple path that is a cycle. Note that the definition of path and cycle applies to directed graph as well . A cycle is a path that begins and ends at the same vertex. Simple cycle is a simple path that is a cycle. Note that the definition of path and cycle applies to directed graph as well.
Disconnected graph Connected graph : there is a path between every pair of nodes This graph is Disconnected . It has two connected components . In a connected graph, there is a path between every nodes. A graph does not have to be connected. The above graph has two connected components . Applications 15 Travel Planning shopping mall direct route 5 cost What is the shortest way to travel between A and B? “SHORTEST PATH PROBLEM” How to minimize the cost of visiting n cities such that we visit each city exactly once, and finishing at the city where we start from? “TRAVELING SALESMAN

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lecture_10_graph_-_3in1_with_notes - Graphs Outline What is...

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