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The whole sentence is "Loneliness is not a function of being alone, but rather, a function of how socially connected you are to those around you".
I don't know why not " how socially you are connected to those around you".It's what I think is usually used.What is the difference between the original sentence and mine?
"How socially you are connected to..." has a slightly different meaning to "How socially connected you are to...". It is the meaning of "how" that is different in each case.
How, used in this way, can have one of two different senses. It can mean "the means by which", or it could mean "the extent to which".
how socially you are connected... equals "the means by which socially you are connected".
how socially connected you are... equals "the extent to which you are socially connected".
