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What's the relation that joins the nodes? Open the image in a new tab if you'd like to see the diagram with better resolution.

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Hint 1

It is equally important to think about why any given two nodes are connected as it is to consider why they are not connected.

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The numbers are connected if the prime representation of them has the same number of primes(can be non-distinct)

Example:

$24=2^3\times3^1$ so there are $3+1=4$ prime factors and $16=2^4$ which has $4$ prime factors so they are connected.
$11=11^1$ so there are $1$ prime factor and $12=2^2\times3^1$ so there are $2+1=3$ prime factors so they are not connected.

I thought it should be nice to include my thinking process:

All the primes are connected to each other. What is the same among the primes?
Oh! They have the same number of factors($2$)!
No, it doesn't applies for some connections.
Each graph is a complete graph.
After a while, I found out the connection between the numbers.

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  • $\begingroup$ Thanks for sharing your thought process! It's cool to see that you overcame the less obvious part of this puzzle. $\endgroup$ – Galen Apr 29 at 5:06

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