Does a higher education cause having less friends?

There's no correlation at all on a 'personable' level! The only thing that MAY influence that appearance is social visibility, which instead of being a social butterfly, an educated person may have a focus for their attention on projects that require deeper thought and thus less time for partying. Conversely, think of those people who go to university and graduate with qualifications that show their ability to learn, but who do not put their learning to use - they have the 'higher education' but just not the focus to use it - yet either they or the 'focused' person may have many or few social friends.
Thirdly: What is a 'friend'? - someone to party with or someone to trust?