Exercises and Assignments
Pen and Paper: Walk It By Hand in Class
You work this in class, with nothing but a pencil. Part 1 comes before any of it is named: you fill in a transition table by hand and guess where a walker spends its time. Parts 2 and 3 come after the lecture, and you check the lecture’s formulas against the numbers you find.
- A Walker with No Map (solutions): four pages in three parts.
- Part 1: four friends, A to D. You write the chance of each move, add up the chances of the three-step routes from A to B, and guess who the walker visits most.
- Part 2: the karate club in the simulator. You find the most and the least visited member, and divide their friendships by 78.
- Part 3: twelve members in two groups of six. You plot the second eigenvector, work out how fast each eigenvalue dies, and explain why a short walk shows the groups and a long walk shows degree.
Interactive Demos
- Ladder Lottery: a fixed board, an unpredictable outcome. One knob sets the rungs; the histogram is where two thousand fresh boards put you, and Gap from even measures it. Drag from four rungs to sixty and watch the gap fall from about 0.6 to 0.08 — that is a random walk mixing, seen from the inside.
- Random walk simulator: the karate club by default. Run five thousand steps and watch every bar settle onto its k/2m mark. Then run it on a network with two obvious communities and count how long the walker stays on one side. Then turn the teleport knob up and find where the distance stops falling.
Assignments
Neither graded assignment runs in this module. The Pair Notebook and the Group Mini-Project both cover Modules 2 through 6. The worksheet and the notebook above are practice, not submissions.