This question came from a user of the new Outlook.com site:
In the People section of Outlook.com, I linked my Gmail, Twitter and LinkedIn contacts. I do not store any Outlook-only Contacts there, they are all linked. I'm syncing to Outlook but none of these linked People are syncing across. Is there any reason why these linked People will not sync with my desktop?
This is normal behavior. The linked contacts are linked on that site only, not synced to Outlook. You can set up the social connector in Outlook and can sign into LinkedIn or Facebook, but Gmail and Twitter will to be exported / imported or you'll need to use sync apps.
See Developing a provider for the Outlook Social Connector for utilities to sync Google contacts. I'm not aware of any apps that sync Twitter contacts to Outlook contacts.
Speaking of Twitter, I've had several queries in recent weeks asking about a Twitter provider for the social connector. At this time, the only connectors available for Outlook 2013 are for Facebook and LinkedIn. A couple of others are available for older versions Outlook, but no Twitter provider. If someone wants to try their hand at it, see Developing a provider for the Outlook Social Connector