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.)

Simulation results: (i)Avg.=17.580618, Std=11.973345, Max.=60(568 times); (ii)Avg.=25.841586, Std=14.029913, Max.=94(9 times)

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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.)

Simulation results: (i)Avg.=45.854342, Std=31.466060, Max.=174(11 times); (ii)Avg.=54.982183, Std=30.635922, Max.=201(1 times)

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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.)

Simulation results: (i)Avg.=65.398325, Std=46.356887, Max.=286(3 times); (ii)Avg.=76.457533, Std=42.649615, Max.=310(1 times)