Homework Help is Here – Start Your Trial Now!
Engineering
Computer Engineering
5. Newman, Networks 2010 15.2) One of the difficulties with the original small-world model depicted in Fig. 15.3a is that vertices can become disconnected from the rest of the network by the rewiring process. For instance, a single vertex can become disconnected if all of its incident edges around the ring are rewired and it has no shortcuts. a) Show that the probability of this happening to any given vertex is [pe^(−p)]^c. b)

5. Newman, Networks 2010 15.2) One of the difficulties with the original small-world model depicted in Fig. 15.3a is that vertices can become disconnected from the rest of the network by the rewiring process. For instance, a single vertex can become disconnected if all of its incident edges around the ring are rewired and it has no shortcuts. a) Show that the probability of this happening to any given vertex is [pe^(−p)]^c. b)

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...
See similar textbooks
icon
Related questions
Question
5. Newman, Networks 2010 15.2) One of the difficulties with the original small-world model depicted in Fig. 15.3a is that vertices can become disconnected from the rest of the network by the rewiring process. For instance, a single vertex can become disconnected if all of its incident edges around the ring are rewired and it has no shortcuts. a) Show that the probability of this happening to any given vertex is [pe^(−p)]^c. b) Hence, how large must the network be before we expect that one vertex will be disconnected, if c = 6 and p = 0.01?
Figure 15.3: Two versions of the small-world model. (a) In the original version of the small-world model, edges are with independent probability p removed from the circle and placed between two vertices chosen uniformly at random, creating shortcuts across the circle as shown. In this example n = 24, c = 6, and p = 0.07, so that 5 out of 72 edges are "rewired" in this fashion. (b) In the second version of the model only the shortcuts are added and no edges are removed from the circle.
Transcribed Image Text:Figure 15.3: Two versions of the small-world model. (a) In the original version of the small-world model, edges are with independent probability p removed from the circle and placed between two vertices chosen uniformly at random, creating shortcuts across the circle as shown. In this example n = 24, c = 6, and p = 0.07, so that 5 out of 72 edges are "rewired" in this fashion. (b) In the second version of the model only the shortcuts are added and no edges are removed from the circle.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Computer Networking: A Top-Down Approach (7th Edi…
Computer Networking: A Top-Down Approach (7th Edi…
Computer Engineering
ISBN:
9780133594140
Author:
James Kurose, Keith Ross
Publisher:
PEARSON
Computer Organization and Design MIPS Edition, Fi…
Computer Organization and Design MIPS Edition, Fi…
Computer Engineering
ISBN:
9780124077263
Author:
David A. Patterson, John L. Hennessy
Publisher:
Elsevier Science
Network+ Guide to Networks (MindTap Course List)
Network+ Guide to Networks (MindTap Course List)
Computer Engineering
ISBN:
9781337569330
Author:
Jill West, Tamara Dean, Jean Andrews
Publisher:
Cengage Learning
Concepts of Database Management
Concepts of Database Management
Computer Engineering
ISBN:
9781337093422
Author:
Joy L. Starks, Philip J. Pratt, Mary Z. Last
Publisher:
Cengage Learning
Prelude to Programming
Prelude to Programming
Computer Engineering
ISBN:
9780133750423
Author:
VENIT, Stewart
Publisher:
Pearson Education
Sc Business Data Communications and Networking, T…
Sc Business Data Communications and Networking, T…
Computer Engineering
ISBN:
9781119368830
Author:
FITZGERALD
Publisher:
WILEY
SEE MORE TEXTBOOKS