No maths degree required.Guide · Graph theory
Your company is a network. It has its weak spots.
Who owns what, what depends on what, what rests on nobody: mathematics has a tool to see it, nearly three centuries old. Here are the four ideas that matter to a business owner, without a single formula.
What is a graph?
Points, and lines between them.
That is all. The points are things, the lines say they are connected. In 1736, Leonhard Euler used it to prove that you cannot cross each of the seven bridges of Königsberg exactly once; today, the same idea runs your GPS, your social networks and transport planning.
In your company, the points are your know-how — invoicing, hiring, selling, running a leadership meeting — and the people who own it. The lines say that one piece of know-how feeds another, or that a person is responsible for it. Drawn this way, what was invisible in a list becomes obvious.
Four ideas
What they say about your company.
01 — Degree
The number of lines leaving a point.
A highly connected point is central: a lot goes through it. On a road network, it is the junction that jams. In a company, it is the person everything goes through, often the owner. While they are there, all is well; the day they are away, everything they own waits.
In Marcel: a person who owns 30% or more of what is written is a bottleneck, in red on the map; at 15%, they are busy, in orange.
02 — The isolated point
A point no line connects.
An isolated point rests on nothing. In your company there are two kinds: the document nobody owns — written once, it grows stale without anyone noticing — and the person who owns nothing written — their know-how exists, but it is nowhere. That is how a company loses what it knows.
In Marcel: every document has an owner, by default whoever wrote it. What is written with no owner, and the people who own no document, light up on the map.
03 — Direction
When a line has an arrow: A feeds B.
Some links have a direction. Your offers feed your quotes, your quotes feed your invoicing. If your offers are written down nowhere, every quote is redone from memory, and invoicing inherits it. What is missing upstream weakens everything that follows: so you start upstream.
In Marcel: our team has linked the Catalogue's skills by hand ("A feeds B"). On the map, each skill shows what it relies on and what it feeds, and the missing essentials light up.
04 — Clusters
Points more connected to each other than to the rest.
A graph splits into clusters: sales, delivery, administration. Each should be owned by a team. A cluster with no team is a domain nobody is in charge of; a document owned by someone from another cluster is sometimes deliberate, often an oversight.
In Marcel: each domain has its colour and its place on the map. Your teams say which domains they cover; I flag a domain with no team, and what is owned outside its domain's team.
On a real map
The four ideas, on the demo company.
Klaris Digital, an agency of fifteen people. Click what jumps out: the bottleneck, the missing essentials, the people with no document.
What the map does not do
Your structure, not surveillance of your team.
Some network analyses read emails, calendars and chat to work out who talks to whom. Marcel's map reads none of that: it reads what is written, and who is responsible for it.
- It is only as accurate as what you have written: a hollow map says, first, that it is time to write
- It judges no one: a bottleneck is a weakness of the company, rarely a fault of the person
- It is read as a team: leadership sees the map, everyone reads the documents according to their rights
Your questions
Do I need to understand the maths to use it?
No. A full dot is written, a hollow dot is not, a person in red owns too much. Everything else is done for you.
Where do I start when the map reveals a bottleneck?
With what that person alone owns and the company needs every week. We write it down with them, then hand it over: a document changes owner in one click.
Where do the links between skills come from?
The meaningful links ("A feeds B") are set by hand by our team. Others are computed: a document that cites another, the same strategy sections read, the same expert drafting them.
Does it work for a company of five?
Yes, and that is often where the map speaks loudest: at five, one person quickly owns half of what matters.
