Armed officers joined those from the counter terrorism command when the arrests were made at about 4am.
Police say the operation was not linked to the Olympics.
A 38-year-old woman was also arrested for alleged fraud offences and two other men were held over alleged immigration offences.
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Accompanied by the Duke of Edinburgh, the Queen will attend the opening ceremony of the fifth session in the Holyrood chamber.
Ms Leadsom has received the backing of Ian Duncan Smith, the former work and pensions secretary.
The former shadow work and pensions secretary is considered a more viable candidate than Angela Eagle, a Labour source has told ITV News.