Fundamentals
“Knowledge graph” sounds technical, and the idea underneath it is not. It is the observation that understanding a subject has always been less about how much you know and more about how the pieces hang together — and that this structure can be written down.
Start here
Think of someone who can work out 20% of 80 without hesitating, but who freezes when asked: a jacket costs 80 euros after a 20% discount, what did it cost before? They know the facts. What they are missing is a connection — that a percentage works in both directions. No amount of re-reading the definition of a percentage will supply it, which is why re-reading rarely helps. The gap is not in the facts. It is in the space between them.
Understanding is not knowing more things. It is knowing how things connect.
What a knowledge graph is
Picture every idea in a subject as a point, and every meaningful relationship between two ideas as a line joining them. That is the whole concept. The points are things worth learning — a definition, a rule, a worked example, a typical mistake. The lines say how they stand to one another. A textbook can only put ideas in a single order, one after another. A map lets you see that this idea depends on that one, that this example illustrates that rule, and that these two things are easy to confuse.
Why the lines carry the meaning
The points in the map are the part people expect. The lines are the part that turns a list into an understanding — and they are exactly the knowledge that experienced teachers hold and rarely get to write down.
You cannot understand percentages without understanding fractions, and you cannot understand fractions without division. Almost every subject is full of these dependencies, and almost none of them are written down anywhere. They live in the head of whoever has taught the subject for fifteen years.
A worked example is not the same kind of thing as the rule it illustrates, and treating them as interchangeable is how learners end up able to follow an example but unable to handle a problem that looks slightly different. The link between the two is a real piece of knowledge.
A price that rises 20% and then falls 20% does not return to where it started. Experienced teachers carry hundreds of these, and they teach toward them deliberately. Most written material never mentions them, because the author no longer finds them surprising.
Rules have exceptions, sources disagree, and later material sometimes overturns earlier material. Somewhere the contradiction has to be recorded as a contradiction, or a learner meets both statements and quietly concludes the subject does not make sense.
Where the idea comes from
This is not a recent invention, and it is worth knowing that, because it tells you the idea is not a technology fashion.
Teachers have always built these maps. A curriculum is one: a claim about what has to be understood before what. So is the sequence a good trainer works out after teaching the same course thirty times and learning where people reliably get lost.
In the 1960s, researchers studying how human memory works proposed that we store meaning as a network of linked concepts rather than as a list of entries — the idea that became known as a semantic network. In the 1970s, the educational researcher Joseph Novak developed concept mapping, in which learners draw their own ideas as labelled points and connections. He found the maps were remarkably good at exposing what a learner actually believed, including the things they had confidently got wrong.
Both traditions arrived at the same conclusion from different directions: the structure is not a summary of the knowledge. The structure is a large part of the knowledge.
Why it matters now
Most tools that promise to make documents useful work by finding passages that resemble your question and writing an answer over them. That is genuinely useful for looking something up, and it is not teaching. A system built that way cannot tell a definition from an example, cannot know which idea has to come first, and cannot notice that the one thing you are missing is three steps further back. It is good at retrieving text. It does not know what the text is.
When someone is stuck on percentages, the useful question is what they are missing underneath. A structure that knows what rests on what turns a vague "struggling with maths" into a specific, fixable thing.
A table of contents has exactly one route through a subject, chosen once for everybody. A web of connections has many valid routes, which is what makes it possible to start from what somebody already knows.
If knowledge is held as a structure built out of real source material, any explanation can be traced back to the page it came from. Something you can check is a different kind of thing from something you have to trust.
Subjects change. Regulations change, and so do methods and best practice. A structure can record that a piece of knowledge has been superseded. A printed course simply goes quietly out of date.
Structure first. Everything useful comes after it.
How we approach it
We build these maps out of the material an institution already owns, and we think how that is done matters as much as that it is done.
Schools, universities and companies are not short of knowledge. It sits in textbooks, handbooks, slide decks and the experience of their best people. The work is to give that material a structure, not to replace it.
Software can propose a structure. It should not be the one that approves it. What gets taught is what an educator has looked at and agreed with, which is both a quality question and a question of who is accountable.
The structure is built from your material and stays yours, connected to the sources it came from. We think of this as a map of what an institution already knows, not as content we supply.
What we do not claim is that this happens by itself. Turning a shelf of material into an honest map of a subject is real work, some of it automated and some of it a person sitting down with the result and disagreeing with it. We would rather say that plainly than describe a button that does it.
Where this leads
Knowing that one idea rests on another is not the same as knowing how to get a particular person from one to the other on a Tuesday afternoon. That is a separate question, with its own body of research behind it.
Read next: adaptive learning science, on what is actually known about how people learn differently, and didactics, on the craft of teaching a thing well. The technology all of this runs on is Atlas.
See it on something you know
The quickest way to judge any of this is to watch your own material laid out as a structure, and to point at the places where it gets your subject wrong.