THE CHINESE UNIVERSITY OF HONG KONG

Department of Mathematics

UGEC2532 The Day After Social Network

Homework 1

Prepared by Jeff Chak-Fu WONG

Due Date: February 14, 2018

Name: Student No.:

Class: Final Result:

I declare that the assignment here submitted is original except forsource material explicitly acknowledged. I also acknowledge that Iam aware of University policy and regulations on honesty in academicwork, and of the disciplinary guidelines and procedures applicable tobreaches of such policy and regulations, as contained on the websitehttp://www.cuhk.edu.hk/policy/academichonesty/

Signature Date

For lecturer’s use only

Graded problems

Score

Total

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[Objective:] The purpose of this homework assignment is, by making useof the directed network and the undirected network, to

• learn how to generate a social network based on two criteria: the

identity of the kind of node in the network and the relation in thenetwork that defines what ties will be included;

• know how to transform the graph (or sociogram) into the adjacentmatrix, the adjacent list, the edge list, and vice versa;

• get used to the basic concepts and terminology of social networks.

Lecturer’s Comments

Question 1

[Problem Description:] Consider three different kinds of mutual friend-

ship networks, as shown in Figures 1, 2, and 3. Do these networks matchyour social life at CUHK?

The rectangular boxes represent people. A line between the names of two

people means that they know each other. If there is no line between twonames, then the people do not know each other. The relationship “know

each other” goes both ways; for example, because Person A knows PersonB, that means Person B knows Person A.

The following three main target persons and their roles in their friendgroups will be studied and discussed:

Group Target Person

Group 1 DonnaGroup 2 John

Group 3 Vera

Figure 1: Group 1: A mutual friendship social network

Figure 2: Group 2: A mutual friendship social network

Figure 3: Group 3: A mutual friendship social network

[Questions:] Answer the following questions:

1. Discuss each target person’s social circle, e.g., what types of friend-

ships exist between a target person and his/her friends.

2. Which group do you need to enter in order for you to get close tothem if someone brings you into their friend circle?

Please share thoughts and opinions freely by writing them on this home-

work. Any opinions and comments are welcome!

Question 2

[Problem Description:] Consider the friendship network shown in Figure

4.

The rectangular boxes represent people. A line between the names of two

people means that they know each other. If there is no line between twonames, then the people do not know each other. The relationship “know

each other” goes both ways; for example, because Person A knows PersonB, that means Person B knows Person A.

Figure 4: A mutual friendship social network

[Questions:] Answer the following questions:

1. Write down the adjacent matrix, the adjacent list and the edge listfor each.

2. Let A be an adjacent matrix and 1 be a |V | × 1 all one vector, where|V | is the total number of nodes. What are the meanings of these

three numbers?k1 =

(

1TA)T

,

k2 = A1

andk3 = 1TA1.

3. We call a path between two vertices with the fewest edges a shortest

path. When a path goes from a particular vertex back to itself, that is

a cycle. List the shortest cycles, the ones that link only three persons.

4. Find the longest path in this network from Person A to Person B. Inother words, how many links will there be?

Question 3

[Problem Description:] Consider the following network of relationships

between members of a group, recorded in a single working day. The networkin Figure 5 shows the flow of information within a dispersed new technology

product development team. In this case each member of the team wasasked “Whom do you turn to for information to get your work done?”The network has been color-coded to identify which team members are in

marketing (in violet), finance (in black) and manufacturing (in blue):

The rectangular boxes represent people. Each line indicates an informationlink between two members; arrows represent the direction of the relation-

ship (incoming arrows show that the person is a source of information;outgoing arrows reveal that the team member seeks information from thelinked parties).

Figure 5: An information flow social network

[Questions:] Answer the following questions:

1. Represent the network in a table (or construct an adjacent matrix),filling it with the number “1” when there is a connection and with “0”

when there is not one.

2. Transform the graph (or sociogram) in Figure 5 into an adjacent listand an edge list. (We shall see that the adjacent matrix and the edge

list will help us plot the graph via NodeXL and R software).

3. Calculate the in-degree and out-degree of each node in the network.

4. Calculate and discuss the density of this network.

5. Discuss who is/are the most prominent person/people and discusshis/her/their role(s).

6. Discuss who is/are the unconnected node(s) and discuss his/her/theirrole(s). In reality, who would these people be and what kinds of jobs

would they have?