Calculating the degree, Betweenness, and Closeness on a Simple network homework

COM 494 Week 5 Assignment: Calculate degree, betweenness, and
closeness on a simple network
Using the following network, fill in the correct values in the tables below. Step-by-step instrunctions.
Degree
To complete the degree table:
1. For each node, count the number of edges connected to it (called incident edges). Enter
this in the “degree” column.
2. For each row, divide this value by the number of nodes minus 1. Enter this in the
“standardized degree” column.
3. Add the standardized degree values to get a sum.
4. For each row, divide the standardized degree value by the sum from the last step, multiply that
by 100, and enter the results in an “as a %” column.
5. Add up the percentages you calculated on the last step. If they don’t add-up to 100 you have
an error in your calculations.
Node
Degree (incident
edges)
Standardized Degree
As a %
A
B
C
D
E
F
Shortest Paths
Take care doing this because it’s used for both the betweenness and closeness
calculations below. To complete the shortest paths table:
1. List all the pairs of nodes in the “pair” column. Hint: This network is the same size as the one
in the writeup, so it will have the same pairs of nodes.
2. For each pair of nodes, find the shortest path between them, and list the nodes in this path
“shortest path” column. Hint: Two of the lines will have more than one shortest path, i.e.
two alternative paths of the same length you could use to get between the two nodes.
3. For each row, count the length of the path, i.e. the number of links in it, and list this in the
“length” column.
Shortest Paths
Line #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Pair
Shortest Path
Length
Betweenness
To complete the betweenness table:
1. For each node, A through F, count the number of times it is between two other nodes in the
shortest paths column of the shortest paths table, and enter this count in the “times
between” column.
a. Ignore cases where the node is at the beginning orend of a path, because it is
not between other nodes in those cases.
b. For cases where this is more than one shortest path, you have to adjust the amount you
add to the count, as described in the writeup.
c. Add the lines where you found the node between others in the “see line #’ col umn
for reference.
2. For each row, divide the “times between” valueby n times (n-2) and divide that product by 2,
where n is the number of nodes in the network. Enterthis in the “standardized
betweeness” column.
3. Add the standardized betweenness values to get a sum.
4. For each row, divide the standardized betweenness value by the sum from the last step, and
multiply by 100. Enter this in the “as a %” column.
5. Add up the percentages you calculated on the last step. If they don’t add-up to 100 you have
an error in your calculations.
Node
Times Between
See Line #
Standardized
Betweenness
As a %
A
B
C
D
E
F
Closeness
To complete the closeness table:
1. For each node, use the shortest paths table and add up the lengths of all the shortest paths
between this node and all the other nodes in the network. Enter this in the “Farness” column,
and put the line numbers from the shortest paths table in the Line # column for reference.
2. For each row, divide 1 by the farness value, and enter this in the closeness column.
3. For each row, multiply the closeness value by the number of nodes in the network minus 1, and
enter this in the standardized closeness column.
4. Add the standardized closeness values to get a sum.
5. For each row, divide the standardized closeness valueby the sum from the last step, multiply by
100, and enter that in the “as a %” column.
6. Add up the percentages you calculated on the last step. If they don’t add-up to 100 you have an
error in your calculations.
Node
A
B
C
D
E
F
Line #
Farness
Closeness
Standardized Closeness
As a %