Node already installed, it's just not linked

I managed to fix this by first running sudo chown -R $USER /usr/local and following it with brew link node. Now I have node properly installed.

This solution works! It is a combination of all the combinations.

Fix it using the following code.

1. sudo chmod 776 /usr/local/lib
2. brew link --overwrite node

   Outputs: Linking /usr/local/Cellar/node/9.6.1... 49 symlinks created

3. sudo chmod 755 /usr/local/lib

If you are on High Sierra, then sudo chown -R $USER /usr/local won't work. Instead use:

sudo chown -R $(whoami) $(brew --prefix)/*

Source: https://github.com/Homebrew/brew/issues/3228#issuecomment-332679274