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Sample questions for Midterm I
Social Network Analysis
1. List all strongly connected components in the graph below?
ANS: A, B, E, CDFJ, GIH,
2. Consider the network below. Find the clustering coefficient distribution and calculate its mean and
standard deviation?
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ANS: The clustering coefficients for all nodes are given below:
1.0000000 0.3000000 0.3333333 0.0000000 0.0000000 0.3333333 0.3333333 1.0000000 0.3333333
0.3333333
The distribution is given below
Coefficient (c)
0
3/10
1/3
1
Frequency (f)
2/10
1/10
5/10
2/10
cf
0
3/100
5/30
2/10
0.3966667
fc^2
0
9/1000
5/90
2/10
0.2645556
Average = 0.3966667
SD =sqrt(0.2645556- 0.3966667^2) = 0.3274311
3.
Consider the network above. Find the degree distribution and calculate its mean and standard deviation?
ANS: Degree distribution
degree (d)
2
3
4
5
Frequency (f)
2/10
5/10
2/10
1/10
df
4/10
15/10
8/10
5/10
3.2
fd^2
8/10
45/10
32/10
25/10
11
Average = 3.2
SD =sqrt(11- 3.2^2) = sqrt(0.76)= 0.8717798
4.
Consider the network above. Find the closeness centrality measures of all nodes.
ANS: 0.05263158, 0.07692308, 0.07142857, 0.06250000, 0.06250000, 0.05882353, 0.06250000,
0.05263158, 0.07142857, 0.05555556
5.
Consider the network above. Find the betweenness centrality measure of all nodes.
ANS: 0.000000, 10.166667, 5.166667,
0.000000, 7.000000, 1.000000
6.
ANS:
3.166667,
Given the following adjacency matrix, draw the graph
a b c d e
a 0 1 0 0 0
b 0 0 1 0 0
c 0 0 0 1 0
d 0 0 0 0 1
e 1 0 0 0 0
4.166667,
1.833333,
3.500000,
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7.
Explain the difference between the regular PageRank and the Scaled PageRank.
ANS: Basic PageRank has the leaking problem where a single node gets all weights, while the scaled
version overcomes this difficulty by a scaling factor to convert the matrix in question into an all-positive
matrix.
8. Explain how the Erdos-Renyi (ER) random network is constructed. And give at least three
network statistical properties that the ER network does not fit the real network very well.
ANS: Each potential link is included into the network independently with a fixed probability.
(1) Degree distribution is normal in contrast to the power distribution for real networks
(2) No community structure in contrast to the community structure for real networks
(3) No homophily in contrast to the homophily for real networks
9. Determine the number of shortest paths between nodes A and B in the following graph:
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ANS: 7*5*10=350
10. What does it mean if a node has high betweenness centrality? Explain by an example.
ANS: More pair of nodes to use this node to communicate as quickly as possible.
11. What does it mean if a node has high closeness centrality? Explain by an example.
ANS: It is quicker for this node to communicate information to all the other nodes
12. What does it mean if a node has high eigenvalue centrality? Explain by an example.
ANS: Not only this node has many nodes, but also it has some important nodes.
13. What does it mean if a node has high PageRank centrality? Explain by an example.
ANS: Not only this node has many outgoing nodes, but also it has some important outgoing nodes
14. Construct a graph with 4 nodes and degree sequence = [5,3,3,3].
ANS:
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15. What is the average path length of the Erdos Renyi (ER) random network with 50 nodes and average degree
of 2?
ANS: <L>=log n / log <K> = log 50 / log 2 = 5.643856