Why does graph density fail?

The most common reason graph density fails: Treating link count as a vanity metric. You can inflate density by creating shallow, meaningless connections — tagging everything with the same broad category, linking notes because they share a word rather than a concept. Density without semantic weight is noise. The test is whether you can explain why each edge exists. If you can't articulate the relationship in a sentence, the link is decoration, not structure.

The fix: Pick two subjects you know well and one you're just beginning to learn. For each, list 10 concepts from memory. Then draw the connections between them — every relationship you can articulate (causes, enables, contradicts, exemplifies, depends on). Count the edges. Calculate the density: edges divided by (nodes times (nodes minus 1) divided by 2). Compare the three numbers. The subject you understand most deeply will have the highest density, not because you tried to connect things, but because deep understanding is dense connection.

The underlying principle is straightforward: A densely connected area of your graph represents deep understanding.