Exercise Questions

Question 1

Answer 1

Question 2

Answer 2

Question 3

Answer 3

Question 4

Answer 4

Question 5

Answer 5

Question 6

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Question 7

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Question 8

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Question 9

Answer 9

A commonly used strategy to randomize a given empirical network is to swap links between two vertices. A randomly chosen pair of links (a-b) and (c-d) are replaced by the pair (a-d) and (c-b). By construction, the degree distribution remains invariant, as neither vertex acquires or looses links.

Question 10

Answer 10

Question 11

Answer 11

Question 12

Answer 12

Question 13

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Question 14

Answer 14

Question 15

What are the limits of an efficient star network in the Connections model?

Answer 15

Question 16

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Question 17

For the Islands connections model, which of the following properties are correct?

(1) Diameter increases proportionally to the total number of nodes, as the num- ber of islands goes up (fixing the number of nodes in each island).
(2) (Relatively) low diameter.
(3) Average degree increases proportionally to the total number of nodes, as the number of islands goes up (fixing the number of nodes in each island).
(4) (Relatively) high clustering.

Answer 17

Question 18

Answer 18

Question 19

Compare the co-author model with the symmetric connections model. Elaborate the difference in externality effects.

Answer 19

Question 20

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Question 21

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Question 22

(both: Poisson & scale-free)

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Question 23

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Question 24

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Question 25

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Question 26

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Question 27

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Question 28

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Question 29

(How to, don’t actually do it)

Answer 29

Simply compute b(t + 1) = T b(t).

Question 30

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Question 31

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Question 32

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Question 33

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Question 34

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Question 35

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Question 36

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Question 37

Answer 37