# What's the graph relation? #2

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.

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.

• Thanks for sharing your thought process! It's cool to see that you overcame the less obvious part of this puzzle. – Galen Apr 29 '20 at 5:06