Association charts, and why counting links finds the wrong person

Give LINK a CSV of who is connected to whom and it draws the chart and computes the measures underneath it: degree, betweenness, bridges and articulation points, all exactly rather than estimated. The layout is seeded from the names, so the same file always draws the same picture. Nothing is uploaded.

A chart drawn by hand shows what you already believed

This is the honest problem with association charts. Somebody who knows the case lays out the nodes, and the people they think are important end up in the middle, large and central, because that is where a human puts important things. The chart then confirms the belief that produced it, and does so persuasively, in a meeting, on a screen.

The value of drawing the chart from a file rather than by hand is not that it is faster. It is that the position of everything is decided by the connections and not by you.

Degree is the least useful measure on the chart

Degree is simply the number of links a person has. It is the first thing anybody looks at and it is almost always the least informative.

The person with forty connections is a switchboard: a taxi office, a shared handset, a sales line, somebody whose job is talking to people. High degree usually means you have found somebody obvious, and often somebody irrelevant.

Betweenness, and the person it finds

Betweenness asks a different question. For every pair of other people in the network, it counts how many of the shortest routes between them pass through a given person.

Somebody connected to everybody scores highly, which is unsurprising. But so does somebody with two or three links who happens to sit on the only path between two groups that otherwise have no way of reaching each other — and on the chart that person is a small node off to one side, easy to pass over.

That is the finding worth having. A broker is the point of failure in a network: remove them and the two halves stop being able to reach each other. Counting connections never finds them. Arithmetic does, and it is the sole reason to compute anything at all rather than just draw a picture.

Bridges and articulation points

Two related findings, precisely defined and often confused with each other:

• A bridge is a link whose removal breaks the network into two pieces. It is the single line holding two groups together.
• An articulation point is a person whose removal does the same.

Both are computed exactly, in one pass of Tarjan's low-link numbering, which is worth saying because both are frequently approximated or eyeballed. They are structural facts about the file, not judgements, and they are the questions most worth asking of a network you do not already understand.

The same file must draw the same chart

A force-directed layout is random unless you make it otherwise, which means the usual behaviour is a chart that rearranges itself every time it is opened. That is fine for exploring and useless as evidence: you cannot put it in a report, you cannot compare it against one made a month ago, and somebody else cannot reproduce it.

So the simulation is seeded from the names in the file and runs a fixed number of rounds. The same data always produces the identical picture. That is not polish — it is the difference between a chart that can be relied on and one that cannot.

What a line means, and what it does not

A line means the file said there was a link. Nothing more. It says nothing about what the link was for, whether it was innocent, or whether the two people at either end have ever met. A network chart is the single most over-read exhibit in this kind of work, precisely because it is visual and looks like a finding, so that caveat belongs next to the findings rather than in a footnote.

Links here are undirected: a call from A to B and a call from B to A are one link with the rows counted. That is the right model for association, which is about who is connected to whom rather than who started it. If direction is the question, the schedule of call data is where it lives.

The short version