LinkedIn Team has sent an email that from 14th December 2011 all InMails and introductions will be sent immediately instead of the usual weekly digest email. If you do not want to set this as your default setting then you change the email preferences using the LinkedIn Settings option.
Login to your LinkedIn Account, click the arrow pointing downwards on the right hand side below your name.
Click the Settings from the drop down list. You may need to sign in to your account again.
Now navigate to Email Preferences and click Set the frequency of emails. In the Frequency of emails window, set the drop down value for InMails, Introductions, and OpenLink as Weekly Digest Email.
Click the Save changes button to confirm and save your setting changes.