Social Media Mining: An Introduction

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CUUS2079-02 CUUS2079-Zafarani 978 1 107 01885 3 January 13, 2014 16:38

2.9 Exercises 49

3. Given the following adjacency matrix, compute the adjacency list and
   the edge list.

A=

⎡

⎢⎢

⎢⎢

⎢⎢

⎢⎢

⎢⎢

⎢⎢

⎢

⎣

011000000

101000000

110110000

001011100

001101100

000110110

000111010

000001101

000000010

⎤

⎥⎥

⎥⎥

⎥⎥

⎥⎥

⎥⎥

⎥⎥

⎥

⎦

(2.29)

Special Graphs

4. Prove that|E|=|V|−1 in trees.

Graph/Network Algorithms

5. Consider the tree shown in Figure2.28. Traverse the graph using both
   BFS and DFS and list the order in which nodes are visited in each
   algorithm.

v 1

v 2 v^3

v 4 v 5 v 6 v 7

v 8 v 9 v 10 v 11 v 12

Figure 2.28. A Sample (Binary) Tree.

6. For a tree and a nodev, under what condition isvvisited sooner by
   BFS than DFS? Provide details.


7. For a real-world social network, is BFS or DFS more desirable? Provide
   details.


8. Compute the shortest path between any pair of nodes using Dijkstra’s
   algorithm for the graph in Figure2.29.


9. Detail why edges with negative weights are not desirable for computing
   shortest paths using Dijkstra’s algorithm.