# SOCI 111 Social Networks Questions

W23 SOCI 111: Social NetworksHomework 1

DUE: 1/25/20; 61 points

Instructions: These problems give you an opportunity to use the concepts and

techniques we’ve learned so far to analyze some toy social systems. They also test your

understanding of basic definitions and procedures. Think of them like exercises; they

help build your network muscles!

I encourage you to work in groups (of no more than 5), though this is not a

requirement. Each student should prepare their own solutions, along with a note at the

top of your assignment crediting other members of the working group. Please make

sure you truly understand the solution to a problem, and please: DO NOT COPY

SOLUTIONS. We will figure it out. In particular, do not go to the testbank at SAC, do not

go to Course Hero, do not use ChatGPT, and do not get solutions from friends who

have taken the course in the past. Likewise, do not create a class-wide GroupMe and

discuss the homework. All of this will impede your learning, and I will treat it as

academic misconduct.

In general, you should show your work rather than just writing down a number. This

makes it easier for us to see that you know what you are doing, and easier for you to

see when you’ve made a trivial mistake. On the other hand, don’t just throw everything

vaguely relevant at the wall and hope that something sticks. You need to be judicious!

Please submit your solutions to your TA at the beginning of class. Your submission

should be neat and legible: you can type it up or write it out by hand, but we aren’t

going to engage in decipherment here. That said, I strongly encourage you to write it out

by hand, as this will prepare you for the midterm and final (which will be handwritten).

Practicing Network Representations

Q1.

Let’s say we wanted to make a network representing the flow of people around

the country during the holiday season. We want to keep track of each leg of travel; not

everyone makes a round trip, and some folks make trips with multiple stops. We care

about movement at the town/city level, so the nodes represent cities. Should this be an

undirected network, or a directed network? Explain your answer. (3 points)

Q2.

Imagine that Zoom kept track of every time two people were on a Zoom call

together. Let’s say we want to create a network where we draw an edge between two

people if, in the past three years, they have been on at least one Zoom call together.

Should this be an undirected or a directed network? Explain your answer. (3 points)

Degree Distributions and Eulerian Paths

Questions Q3 – Q6 refer to the following graph:

Q3.

Plot the degree distribution for this graph. Recall that the degree of a node is

the number of neighbors it has. The degree distribution of a network shows the fraction

of nodes in the network that have degree 0, degree 1, degree 2, degree 3, etc. The

degree distribution is usually plotted with degree on the x-axis (starting at zero and

counting up) and fraction of nodes having degree k, often denoted p(k) on the y-axis.

Hint: Ask yourself how many nodes in this network have 0 neighbors? How many have 1

neighbor? How many have 2 neighbors? Etc. (3 points)

Q4.

From the degree distribution and the total number of nodes in the network, I can

figure out the degree count; from the degree count, I know that it is not possible to find

a path on this graph that crosses every edge, and crosses each edge only once. (Recall:

this is technically called an “Eulerian path”). Why can you be sure that an Eulerian path

is impossible? (3 points)

Q5.

This graph currently has a single component. By deleting one of two possible

edges, I can assure that the resulting graph has two components. Please say what edge

to delete, and explain why the resulting graph has two components. (3 points)

Q6.

Name a path, a simple path, and a cycle on this network! Each one should have

at least four nodes. (3 points)

More fun with adjacency matrices!

Q7.

Consider the following adjacency matrix. Is this network directed or undirected?

How do you know (without drawing the network)? (3 points)

A

0

1

1

0

0

[0

B C

1 1

0 1

1 0

0 1

1 1

1 1

D

0

0

1

0

0

0

E

0

1

1

0

0

1

F

0

1

1

0

1

0]

Q8.

How many nodes are in this network? How many links? Note: You can answer

these questions without drawing the network. (3 points)

Q9.

Now draw the network corresponding to the adjacency matrix in Q7. (3 points)

Q10-Q12 concern the following network:

Q10.

Write down the adjacency matrix for this network. (3 points)

Q11. The in-degree of a node is the number of other nodes that point to it; hence the

in-degree of B is 1. The out-degree of a node is the number of other nodes that it points

to; hence the out-degree of B is 3. Write down the in- and out-degrees of all the other

nodes in the network. (3 points)

Q12. Now we will explore some interesting properties of the adjacency matrix. What

happens when you add up all the entries in a given row (e.g., what happens when you

add up all the entries in the first/top row, row A)? What happens when you add up all

the entries in a given column (e.g., what happens when you add up all the entries in the

first/left-most column, column A)? Compare these answers to your answers in Question

11. Do you notice anything interesting? Can you guess a general rule that relates the

row or column sums of an adjacency matrix to the in-degrees or out-degrees? (3 points)

Q13. Write down the formula for the maximum number of edges in an undirected

network with n nodes. How would you change this to express the maximum number of

edges in a directed network with n nodes? Explain your reasoning. (3 points)

Clustering and collaboration

Q14-Q15 concern the following network of scientists. Each link represents a

collaboration:

Q14. The diameter is the largest distance in the graph. What is the diameter of this

graph? Show a breadth first-search illustrating this longest path. (3 points)

Q15.

What is the clustering coefficient of node C? Please show your work. (3 points)

Q16. Explain, in your own words, one reason why triadic closure occurs. Give an

example. (3 points)

Q17. Explain, in your own words, a second reason why triadic closure occurs. Give an

example. (3 points)

Extreme Erdős

Q18. As you will soon find out, I have an Erdős number of 4. Let’s say that I collaborate

with someone who has an Erdős number of 5. Would this make my Erdős number

lower? How about if I collaborate with someone who has an Erdős number of 2? Is there

any way I could get an Erdős number of 1? Make sure to explain your answer. (5 points)

vs.

Q19. Remember Stranger Things? Consider two actors from this 80’s nostalgia-fest:

Winona Ryder (Joyce Byers, left), who has been in many movies/TV shows, and Millie

Bobby Brown (Eleven, right) who has been in only a few. Which do you think is larger:

The average “Ryder-number” or the average “Brown-number,” where both are defined

like the Bacon number or the Erdős number? Explain your answer. (5 points)

## We've got everything to become your favourite writing service

### Money back guarantee

Your money is safe. Even if we fail to satisfy your expectations, you can always request a refund and get your money back.

### Confidentiality

We don’t share your private information with anyone. What happens on our website stays on our website.

### Our service is legit

We provide you with a sample paper on the topic you need, and this kind of academic assistance is perfectly legitimate.

### Get a plagiarism-free paper

We check every paper with our plagiarism-detection software, so you get a unique paper written for your particular purposes.

### We can help with urgent tasks

Need a paper tomorrow? We can write it even while you’re sleeping. Place an order now and get your paper in 8 hours.

### Pay a fair price

Our prices depend on urgency. If you want a cheap essay, place your order in advance. Our prices start from $11 per page.