Association charts, and why counting links finds the wrong person
The person with the most connections is usually the obvious one. The person worth finding has three connections and sits on the only path between two groups, and on the chart they look unimportant. Only arithmetic finds them.
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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
| The job | Here | Notes |
|---|---|---|
| Betweenness, computed exactly | Yes | A breadth-first pass per person, not an estimate |
| Bridges and articulation points | Yes | One pass of Tarjan's low-link numbering |
| The same chart every time | Yes | Seeded from the names, fixed number of rounds |
| Hide people below a link count | Yes | The measures below stay computed on the whole network |
| Odd headings, two columns | Yes | The first two columns are used if nothing is recognised |
| Low thousands of people | Yes | Betweenness is the expensive part, and it is exact |
| Out as SVG, analysis and CSV | Yes | All written by the tab |
| Say what a link was for | No | A line means the file said there was one |
| Direction of contact | No | Undirected on purpose; the call schedule keeps direction |
| Tell you who matters | No | It tells you who is structurally placed to; that is different |
Questions people ask about reading an association chart
Why is the number of links the least useful measure?
Because the person with forty connections is usually a switchboard: a taxi office, a shared handset, a sales line, somebody whose job is talking to people. High degree generally means you have found somebody obvious, and often somebody irrelevant. It is the first figure anybody looks at and the one least likely to tell them something they did not know.
What is betweenness, and what does it find?
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 with two or three links and a high score is sitting between groups that have no other way of reaching each other (a broker, the point of failure in the network) and on the chart they look unimportant, a small node off to one side. Counting connections never finds them. That is the whole reason to compute anything rather than just draw a picture.
What is the difference between a bridge and an articulation point?
A bridge is a link whose removal breaks the network into two pieces. An articulation point is a person whose removal does. Both are structural facts about the file rather than judgements, and both are computed exactly here, in one pass of Tarjan's low-link numbering, rather than eyeballed off the chart.
Why does the same file always draw the same chart?
Because a force-directed layout is random unless you make it otherwise, and a chart that rearranges itself every time cannot go into a report, cannot be compared with one made a month ago and cannot be reproduced by anybody else. The simulation is seeded from the names in the file and runs a fixed number of rounds, so the picture is identical every time.
What does a line on the chart actually mean?
That 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 most over-read exhibit in this kind of work precisely because it is visual and looks like a finding.
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