The very simple and basic clone will have:
-profile : only 4 text fields (60000 char each): 2 publics, 1 only visible by connections, 1 private. These field must be in HTML editable by embedding FCKeditor (or another editor) + 1 picture (480x640 max, displayed in thumbnail but zoomable)
-Searching capability in all the public fields (plain text)
-Each profile has to be able to be connected with other profiles (as linkedin, this number is unlimited). Invitations are sent by php mail() function.
-style the same as joomla css. The script must accept any joomla css style (but not embed joomla). Start with beez.
-Registering with catpcha (no email confirmation)
-all data in 1 sql database (except jpg pictures)
-each profile must produce a rss flux that summarize all linked profiles activities.
Just a small complement : Even if I make reference to linkedin this project is very simple (I could do that by myself in 2-3 days but I've no time for it and I'm not very good in css):

1 page to edit profile and embed FCKEditor
1 page for user subscription (incl captcha)
1 page for search+1 page to display results
1 page to display profile

in term of script:
-Subscribe name+firstname+location+email (php, add a user to sql database, check the captcha)
-profile : record profile in database, upload picture
-search : display names and allow user to request connection (captcha required). if connection send a mail to user to accept/deny if accept add connection to the two users

additionally, I'd appreciate a stat page that compute the number of possible connections at level 5.