Exam 1

1. Question

   In this network, identify the following:

   • V: Nodes (or Actors or Vertices)
   • E: Edges (or Ties)

   

   
   
   1. $$\begin{aligned} V = & \{Alice, Bob, Carol, Ted\} \\ E= & \{(Alice, Bob),\\ & (Bob, Carol), (Bob, Ted),\\ & (Carol, Bob), (Carol, Ted),\\ & (Ted, Alice), (Ted, Bob), (Ted, Carol)\} \end{aligned}$$
   2. $$\begin{aligned} V = & \{Alice, Bob, Carol\} \\ E = & \{(Alice, Ted),\\ & (Bob, Carol), (Bob, Ted),\\ & (Carol, Bob), (Carol, Ted),\\ & (Ted, Alice), (Ted, Bob), (Ted, Carol)\} \end{aligned}$$
   3. The graph has no nodes and edges
   4. $$\begin{aligned} V = & \{Alice, Bob, Carol, Ted\} \\ E = & \{(Alice, Ted),\\ & (Bob, Carol), (Bob, Ted),\\ & (Carol, Bob), (Carol, Ted),\\ & (Ted, Alice), (Ted, Bob), (Ted, Carol)\} \end{aligned}$$
   
   

   Solution

   $$V=\{Alice, Bob, Carol, Ted\}$$

   $$E=\{(Alice, Ted), (Bob, Carol), (Bob, Ted), (Carol, Bob), (Carol, Ted), (Ted, Alice), (Ted, Bob), (Ted, Carol)\}$$

   
   
   1. False
   2. False
   3. False
   4. True
   
   

2. Question

   Represent this network in matrix format.

   

   
   
   1. 
   2. Matrix representation is not possible
   3. 
   4. 
   
   

   Solution

   $$E=\{(Alice, Ted), (Bob, Carol), (Bob, Ted), (Carol, Bob), (Carol, Ted), (Ted, Alice), (Ted, Bob), (Ted, Carol)\}$$

   

   
   
   1. False
   2. False
   3. True
   4. False
   
   

3. Question

   What is the in-degree and out-degree of node “Bob.”

   

   
   
   1. Out-degree: 0, In-degree: 2
   2. Out-degree: 2, In-degree: 0
   3. Out-degree: 2, In-degree: 2
   4. Out-degree: 1, In-degree: 2
   
   

   Solution

   

   
   
   1. False
   2. False
   3. True
   4. False
   
   

4. Question

   What is the closeness centrality of node D?

   (Hint: Closeness centrality indicates how close a node is to all other nodes in the network. It is calculated as the average of the shortest path length from the node to every other node in the network.)

   

   
   
   1. 1.4
   2. 1.7
   3. 1.6
   4. 0
   
   

   Solution

   Node	Shortest.Path.from.node.D.to
   A	3
   B	2
   C	1
   E	1
   F	2
   G	2
   H	1

   Thus, closeness centrality of node D = $\frac{3+2+1+1+2+2+1}{7} = \frac{12}{7} = 1.7$

   
   
   1. False
   2. True
   3. False
   4. False