You wrote “meaning of words and concepts”, which was already a pretty wild phrase mixing up completely different ideas…

A word is a lexical unit, whereas a concept consists of 1) a number of short designations (terms, usually words, possibly various symbols) that stand for 2) a longer definition (created traditionally through the use of other terms, a.k.a. words).

> I'm talking about the mental structures we build on top of those

Which are always backed by experience of reality, even the most “abstract” things we talk about.

> You'll find the only way you can do it is by relating it to some other concepts

Not really. There is no way to fully communicate anything you experience to another person without direct access to their mind, which we never gain. Defining things is a subset of communication, and just as well it is impossible to fully define anything that involves experience, which is everything.

So you are reiterating the idea of organising concepts into graphs. You can do that, but note that any such graph:

1) is a lossy map/model, possibly useful (e.g., for communicating something to humans or providing instructions to an automated system) but always wrong with infinite maps possible to describe the same reality from different angles;

2) does not acquire meaning just because you made it a graph. Symbols acquire meanings in the mind of an experiencing self, and the meaning they acquire depends on recipient’s prior experience and does not map 1:1 to whatever meaning there was in the mind of the sender.

You can feel that I am using a specific narrow definition of “meaning” but I am doing that to communicate a point.