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The adjacency matrix is a useful graph representation for many analyt- ical calculations. However, when we need to store a network in a computer, we can save computer memory by offering the list of links in a Lx2 matrix, whose rows contain the starting and end point i and j of each link. Construct for the networks (a) and (b) in Figure 2.20:

The adjacency matrix is a useful graph representation for many analyt- ical calculations. However, when we need to store a network in a computer, we can save computer memory by offering the list of links in a Lx2 matrix, whose rows contain the starting and end point i and j of each link. Construct for the networks (a) and (b) in Figure 2.20:

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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2.3. Graph Representation The adjacency matrix is a useful graph representation for many analyt- ical calculations. However, when we need to store a network in a computer, we can save computer memory by offering the list of links in a Lx2 matrix, whose rows contain the starting and end point i and j of each link. Construct for the networks (a) and (b) in Figure 2.20:
Transcribed Image Text:2.3. Graph Representation The adjacency matrix is a useful graph representation for many analyt- ical calculations. However, when we need to store a network in a computer, we can save computer memory by offering the list of links in a Lx2 matrix, whose rows contain the starting and end point i and j of each link. Construct for the networks (a) and (b) in Figure 2.20:
Figure 2.20 Graph Representation (a) Undirected graph of 6 nodes and 7 links. (b) Directed graph of 6 nodes and 8 directed 6 6 links. (a) The corresponding adjacency matrices. (b) The corresponding link lists. (c) Determine the average clustering coefficient of the network shown in Figure 2.20a. (d) If you switch the labels of nodes 5 and 6 in Figure 2.20a, how does that move change the adjacency matrix? And the link list? (e) What kind of information can you not infer from the link list representation of the network that you can infer from the adja- cency matrix? (f) In the (a) network, how many paths (with possible repetition of nodes and links) of length 3 exist starting from node 1 and end- ing at node 3? And in (b)? (g) With the help of a computer, count the number of cycles of length 4 in both networks.
Transcribed Image Text:Figure 2.20 Graph Representation (a) Undirected graph of 6 nodes and 7 links. (b) Directed graph of 6 nodes and 8 directed 6 6 links. (a) The corresponding adjacency matrices. (b) The corresponding link lists. (c) Determine the average clustering coefficient of the network shown in Figure 2.20a. (d) If you switch the labels of nodes 5 and 6 in Figure 2.20a, how does that move change the adjacency matrix? And the link list? (e) What kind of information can you not infer from the link list representation of the network that you can infer from the adja- cency matrix? (f) In the (a) network, how many paths (with possible repetition of nodes and links) of length 3 exist starting from node 1 and end- ing at node 3? And in (b)? (g) With the help of a computer, count the number of cycles of length 4 in both networks.
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