Exercises and Assignments

Build the Paradox Yourself

Ten people, and you decide who knows whom by clicking pairs. Two averages are kept side by side: how many friends the average person has, and how many the average friend has. The friendship paradox, built by hand.

Questions to consider:

• Can you build a network in which the paradox is absent — where your friends have exactly as many friends as you? How many such networks are there?
• Try to make the gap negative. What stops you, and what does that tell you about \text{Var}(k)/\langle k \rangle?
• Which shapes blow the gap up? Compare the ring and the star buttons, then try to beat the star.

Who Do You Vaccinate?

A hundred and twenty people, a disease that spreads along friendships, and a slider for the number of doses. Three strategies run against each other on the same population. Who do you vaccinate?.

Questions to explore:

• Picking people at random reaches people with how many friends on average? Asking a stranger to nominate one friend reaches how many? Match both numbers to a formula from the lecture.
• At twelve doses, how many percentage points of the population does nominating a friend save over picking at random?
• Vaccinating the biggest hubs beats both. What would you have to know about the population before you could do it?

Pen and Paper: Reading Heavy Tails

You work this in class, before the plotting section; it is much less interesting afterwards.

• Reading Heavy Tails (handed out in class; the PDF is being rewritten): how a degree distribution is drawn and how easily a drawing can mislead. You estimate ratios of lengths, areas and volumes by eye, redraw one histogram under two different bin widths, place numbers on a logarithmic scale by hand, and read a CDF and a CCDF.

Assignments

Pair Notebook

Work through this module with the AI tutor and hand in the notebook that the session builds. What is graded is your reasoning, not your code — see the Pair Notebook guide for the setup and a walkthrough of a full session.

• Repository for M04: coming soon. Your invitation link arrives through Classroom 50.

Group Mini-Project

Groups of up to three. One repository per group, graded once, with the same score going to every member of the group. Read how a mini-project runs first — exactly one person accepts the assignment and invites the rest, and that is the step teams get wrong.

• Repository for M04: adv-net-sci-mini-proj-node-degree. Accept the invitation through Classroom 50 first — the repository is not public, so the link only opens once you are enrolled.

Readers who are not enrolled in SSIE 641 cannot open the assignment repositories. The worksheet above and the hands-on notebook cover the same material and need no enrollment.