Haute Lumière

Commerce · II.05 · MMXXVI · daylight

La Bourse  /  Volume II  /  Nº II.05  /  Workbook — the student

WORKBOOK — THE STUDENT

Chapter II.05 · Complexity and Economic Networks

For the person studying this alone, or in a seminar, with no institution to map yet. You have a considerable advantage: everything in this chapter can be computed on a laptop with no libraries, and you are the only reader with the time to actually do it.

---

WHY THIS WORKBOOK IS DIFFERENT

The chapter was written for someone with a counterparty list and a risk committee. You may have neither, and it would be easy to conclude that network economics is something you study now and use later.

That is exactly backwards. Network reasoning is a way of looking, and the looking is learned on small systems. A reading list, a seminar group, a shared flat, a codebase, a band, a family — each is a network with degrees, an assortativity, articulation points and cascade behaviour, and each is small enough that you can draw it completely and check your reasoning against reality within a week. You cannot do that with a banking system. You will never again have access to systems this legible.

So you will do exactly what the executive does. You will simply do it on networks you can see all of.

---

PART ONE — DISCOVERY

Weeks 1–4: draw graphs, by hand, until the shapes are familiar

Exercise 1.1 — Three graphs from your own life (two hours)

Draw three networks completely. Nodes and links, on paper, no software.

1. Your information network. Every source you read regularly, with a link between two sources if one routinely cites or responds to the other.
2. Your money network. Every place money comes from and goes to in a month, with links where one flow depends on another.
3. Your capability network. Every skill you have, with a link between two skills if one is required to practise the other.

For each, write down the number of nodes, the number of links, and the degree of every node. Compute ⟨k⟩ and ⟨k²⟩ by hand. Then compute κ.

The question to sit with: in which of your three graphs is κ closest to ⟨k⟩, and in which is it furthest? The one where it is furthest is the graph where a single removal will hurt you most.

Exercise 1.2 — Find your articulation points (one hour)

An articulation point is a node whose removal disconnects the graph. Find them by brute force: cover each node in turn and ask whether the rest still hangs together.

Write the list. For each one, write a single sentence: what would actually happen, in the first week, if this were gone? Do not write a plan. Just the sentence. You are building the habit of seeing structure before seeing solutions.

Exercise 1.3 — Read one primary source all the way through (three hours)

Take Vitali, Glattfelder and Battiston (2011), The Network of Global Corporate Control. It is open access, it is fourteen pages, and it is readable by anyone who has finished Part One of this workbook.

Read it for the method, not the conclusion. Write down: what was the data source, what was excluded, how was control defined, and what did the authors themselves say the limitations were. Then write one paragraph on the difference between what the paper claims and what the paper is usually reported as claiming.

This is the single most valuable habit in the whole edition. A student who reads one primary source per chapter for seventy-seven chapters ends with something no summary can give.

---

PART TWO — THE ARITHMETIC

Weeks 5–8: compute before you argue

Exercise 2.1 — Reproduce the thresholds (three hours)

Open lib/verify/II_05.py and run it: python3 lib/verify.py II.05. Everything in the chapter prints, with its inputs.

Now do not trust it. Reproduce four numbers independently — on paper, in a spreadsheet, in a different language, anything that shares no assumption with the module:

• κ for a Poisson network with mean degree 6.00. (You should get 7.000.)
• f_c random for that network. (83.33 percent.)
• κ for a power law with exponent 2.6 between two and a thousand. (29.124.)
• f_c random for that. (96.44 percent.)

If you get a different answer, do not assume you are wrong. Find out which of you is. Checking a published computation and disagreeing with it is a real skill and this is a safe place to practise it.

Exercise 2.2 — Run the cascade, then break it (four hours)

The cascade in the module is forty lines. Copy it into a file of your own and change things:

• Make the equity buffers unequal — some banks at 0.50 units, some at 2.00. Does the complete network still have a cliff? Where?
• Add a second shock, arriving a week later at a different bank.
• Make the ring a ring with chords — each bank lends to its neighbour and to the bank four places along. Where does that sit between ring and complete?
• Try three islands instead of two. Then five.

Write down what surprised you. At least one thing will, and the one that surprises you is the one you now understand.

Exercise 2.3 — Estimate a tail index (three hours)

Take any dataset of losses, delays or failures you can get — your own late deliveries, a public dataset of insurance claims, the file sizes in a directory, earthquake magnitudes. Sort it descending. Apply the Hill estimator:

  α̂  =  1  +  n / Σ ln(kᵢ / k_min)

over the tail above some k_min. Now do the thing that matters: vary k_min and watch α̂ move. Plot it. You will discover that tail-index estimation is far less stable than its use in argument implies, and you will never again quote one without an interval.

Exercise 2.4 — The α\* calculation, by hand (one hour)

Derive α* = ln((n−1)/(n/2−1)) / ln 2 yourself, from the two expected-default expressions. Then compute it for systems of ten, twenty, fifty and a hundred banks. Does the crossover get more or less demanding as the system grows? Write one paragraph on what that implies.

---

PART THREE — DREAM AND DESIGN

Weeks 9–12: build something that reads a network

Exercise 3.1 — Build the four-number report (six hours)

Write a single program that takes an edge list and prints exactly four things: κ, f_c random, f_c targeted, and r. Nothing else. No plot, no summary, no interpretation.

Constraints, and they are the lesson: standard library only, under 150 lines, and it must state its denominator — how many nodes and links it read, and what it ignored. A tool that reports a number without saying what it did not look at is a tool that will eventually lie to you quietly.

Exercise 3.2 — Point it at three real networks (four hours)

Edge lists you can obtain legitimately in an afternoon: the co-authorship graph of a subfield from a bibliographic database; the import-export pairs of twenty countries from a public trade dataset; the dependency graph of a software package you use. Run your four numbers on each.

Then write, for each, one paragraph answering: if I wanted to break this, where would I start, and how many nodes would it take?

Exercise 3.3 — The firebreak argument (two hours)

Choose something in your own life that is currently fully connected — one bank account for everything, one laptop holding everything, one friendship group carrying every kind of support. Write a one-page argument for a firebreak, using the arithmetic: what is the shock distribution, what is your estimate of its tail index, what does the compartmented version cost, and what does it save.

Then decide. Either build the firebreak or write down why the arithmetic did not support it. Both are successful outcomes of this exercise. The failure outcome is deciding without computing.

---

PART FOUR — DESTINY AND DELIGHT

Weeks 13–15: make it a habit, and enjoy it

Exercise 4.1 — The standing graph (ongoing)

Pick one of your three graphs from Exercise 1.1 and commit to redrawing it once a month for a year. Same conventions, same page size, dated. Keep them in order.

By month four you will start seeing motion rather than structure, and motion is where the interesting questions live: which nodes are gaining degree, which links have quietly disappeared, whether your κ is rising. A single network diagram is a photograph. A series is a study.

Exercise 4.2 — Teach one brief (three hours)

Take any one of the ten concept briefs and teach it to someone who does not study this — twenty minutes, one worked example, no jargon they have not been given. Brief 3 and Brief 8 work best out loud.

Notice which part you cannot explain. That is the part you do not yet understand, and finding it is the point of the exercise.

Exercise 4.3 — The pleasure of the first drawing (one hour)

Draw a network you belong to and did not choose — a family, a course, a town — and find yourself on it. Sit with where you are. Most people are surprised.

Do not analyse it. This one is not an exercise in reasoning. It is the thing the chapter's Delight movement is about: the recognition of a structure you have been inside for years, seen all at once.

---

Exercise 4.4 — The second reading (two hours)

Swap term projects with somebody in your seminar and try to falsify theirs, not confirm it. Take a route that shares no assumption with theirs: if they computed κ in Python, compute it in a spreadsheet; if they took the edge list from one system, sample ten links and verify them against another.

Ask four questions, in this order, and write the answers down for them.

1. Who will actually use this? Not the marker — the person who runs the thing they mapped. Does the output work for that reader?
2. What did the number not look at? Find the boundary sentence. If there is not one, that is the finding.
3. Is the correction itself a claim? If they found and fixed a fault, has anybody checked the fix?
4. Is this a gap or a boundary? A system that refuses a connection on purpose is not broken. Count a door as a door.

You will find something. Almost every project has one real fault, and almost none of them are found by the person who wrote it — that is structural, not a comment on anybody's ability. The author is the one person who cannot see it.

---

THE TERM PROJECT

One network, carried the whole way

The brief. Choose one real network you can obtain complete data for, and carry it through every movement of the chapter. Not a famous one — a small one you have access to.

Good choices: a student society's committee and its links to other societies; the suppliers of a single small business that will talk to you; the citation graph of thirty papers in a narrow topic; a local sports league's transfer history; the contributor graph of an open-source project.

What you produce, over the term.

1. The edge list, with its boundary explicitly stated. What did you leave out, and why? This is the denominator and it is marked as heavily as the analysis.
2. The four numbers, computed with your own program from Exercise 3.1, with a second independent check of at least one of them.
3. A cascade, defined appropriately for the domain — a default, a departure, a withdrawal of funding, a retraction — run on at least three wirings.
4. An honest negative. One condition under which your network's apparent robustness fails, or one place where the method you used gives the wrong answer. No project is accepted without one.
5. One page for a decision-maker. Whoever actually runs the thing you mapped. What you found, what it implies, and the one action you would take. If they will read it, send it.

Length. The analysis is as long as it needs to be; the page for the decision-maker is one page and that is a hard constraint. Most of the learning happens in the compression.

---

SELF-ASSESSMENT

Score yourself honestly. Nobody sees this.

Any row still in the first column after fifteen weeks names your next week.

---

CARRYING IT FORWARD

Three things from this chapter you will use for the rest of your working life, whatever you end up doing.

First: ask for the edge list. In any organisation, in any analysis, the question who is connected to whom is almost never asked and is almost always answerable from data that already exists. Being the person who asks it is a durable professional advantage.

Second: state the denominator. Every number you produce, for the rest of your life, should arrive with what it did not look at. This will make you slower and more trusted, in that order.

Third: separate the two words. Diversification is what one actor does to its own position. Diversity is a property of the collection. Nearly every argument you will hear about resilience confuses them, and you now have the arithmetic to tell them apart — including the number, 1.0780, at which the advice reverses.

---

APPRECIATIVE QUESTIONS FOR YOUR SEMINAR

1. When has one of us successfully reproduced a published number and found a disagreement? What did we learn about how to check things?
2. Which network that we each drew surprised its author most, and what made it surprising?
3. If our seminar were a network, what shape is it — and what would it take for more of us to be connected to more of us?
4. What is the smallest real network any of us could get complete data on this month, and who would help us get it?