EE6605 HW#5 Solutions 2020
5-1 (i) Ranking: (a) < (b) < (c) < (d) < (e). Here, A < B means A is weaker than B.
(ii) No. The edge betweenness values of the motifs are not proportional to the above ordering.
5-2
(i) 𝑤12 = 6 𝑤15 = 6 𝑤23 = 6 𝑤25 = 9 𝑤34 = 6 𝑤45 = 9 𝑤46 = 3
(ii) 𝑑12 =1/6 𝑑15 =1/6 𝑑23 =1/6 𝑑25 =1/9 𝑑34 =1/6 𝑑45 =1/9 𝑑46 =1/3
(iii) If the "weight" on the connection between two AS is large, then it means that there are more data traffic between them. But in this case, the above-defined "distance" between the two AS is shorter; hence they are "closer" in the sense of having more data-exchange, namely having more business.
5-3
(a) (b) (c) (d) In terms of graph topology:
(a) and (b) are isomorphic; (c) and (d) are isomorphic. In terms of data routing:
(c) = (d) is better than (a) = (b),
because the outer-loop traffic can go through the inner-loop faster in the former.
5-4
(a) C = 3
(b) CC = 3/10
(c) W = √5x5 = 5
5-5
Advantages
Disadvantages
(a)
wide coverage, low cost (less cables)
fragile against attacks
(b)
robust against attacks
small coverage, costly (more cables)
(c)
robust, cost-effective Overall better than (a) and (b)
trade-off of robustness and cost (neither is the best)