Simulation 1.

Descriptions:
1. In the S_5 network( 120 nodes, 240 links)
2. Randomly generate 4,000,000 instances of node pairs (source s, destination d) and s != d
3. For each instances, calculate the path length of (s, d) under
    (i) no failure
    (ii) a single component failure
4. Calculate three statistical quantities: the average path length (Avg.), the standard deviation of path length (Std), and the maximum path length and the number of its occurrences (Max.)
5. Calculate the number of times the fault falls into (s, d)

Simulation results: (i)Avg.=17.582187, Std=11.978795, Max.=60(568 times); (ii)Avg.=average=18.138744, Std=12.780189, Max.=94(2 times), the fault falls into (s, d)=590985 times (14.77%)

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Simulation 2.

Descriptions:
1. In the S_6 network( 720 nodes, 1800 links)
2. Randomly generate 4,000,000 instances of node pairs (source s, destination d) and s != d
3. For each instances, calculate the path length of (s, d) under
    (i) no failure
    (ii) a single component failure
4. Calculate three statistical quantities: the average path length (Avg.), the standard deviation of path length (Std), and the maximum path length and the number of its occurrences (Max.)
5. Calculate the number of times the fault falls into (s, d)

Simulation results: (i)Avg.=45.850862, Std=31.476077, Max.=174(15 times); (ii)Avg.=45.701635, Std=30.989634, Max.=197(1 times), the fault falls into (s, d)=254379 times (6.36%)

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Simulation 3.

Descriptions:
1. In the S_7 network( 5040 nodes, 15120 links)
2. Randomly generate 4,000,000 instances of node pairs (source s, destination d) and s != d
3. For each instances, calculate the path length of (s, d) under
    (i) no failure
    (ii) a single component failure
4. Calculate three statistical quantities: the average path length (Avg.), the standard deviation of path length (Std), and the maximum path length and the number of its occurrences (Max.)
5. Calculate the number of times the fault falls into (s, d)

Simulation results: (i)Avg.=65.340238, Std=46.300390, Max.=288(1 times); (ii)Avg.=65.206945, Std=46.050184, Max.=289(1 times), the fault falls into (s, d)=51687 times (1.29%)