The launch of the highly differentiated LinkedIn networking community prompts an update the Social Networking Models table:

• You can only browse and search members of your network, a few degrees away
• The only way to connect to another member of the network is through a real person providing a referral
• The referral structure prevents spam
• Besides connections made by referral, the only way a connection can be made is by inviting someone by knowing their email address
• The only connections are confirmed ties (both participants agree)
• Therefore:
  • Connections have real meaning
  • Information flow is governed by participants who risk their reputation

IMHO, LinkedIn is the ideal social networking model for business networking.  Because of the constraints imposed it will be successful in attracting serious professionals who have yet to participate in other models. 

When you get your first meaningful referral request, you can't help but consider the reputation you are putting at risk.  My first was an employer wishing to contact a candidate for hire.  The employer was linked to my business partner Ed, then to me and then to an executive I plan on doing business with in the future and finally to the candidate.  Of course I trust Ed, that's why we have a connection.  I also have a level of trust with the executive, and I wouldn't approve the referral unless I was willing to take the risk of believing in my connections.  The structure is amazingly similar to how business networking works in the real world.  Only with an efficient tool.

Take pictures, for example.  While I agree with Liz that the visual makes it a richer social experience, many people have real problems posting their photos online.  Making it a requirement presents a barrier for participation.  And in business looks supposedly don't matter as much as in dating.

Requiring an upgrade to release contact information of someone you were referred to is reasonable.  LinkedIn has a right to make money.  Keeping in mind that it's in Beta, it would be good to make this constraint explicit before someone initiates a referral.

Clay observed a power-law pattern emerging within LinkedIn.  This is a temporary phenomenon, as the system's constraints work against preferential attachment.  Unlike the web where links are boundless, people intermediate.  As Duncan Watts observed, as you ratchet up the requirements for connections the connections diminish.  Hubs will be protected by others and the hubs themselves will limit their connections to the meaningful to prevent being spammed and reputation risk.  The result will be clusters of social networks with a more random distribution of link scale, reasonably maxing out at 150 connections per person.

Because the requirements for connections are high the network will not grow as fast as other systems, but the network's value will be higher because of its web of trust. 

UPDATE: The discussion on LinkedIn, like with most of Joi's comment section, is getting really interesting.  Reid, the CEO of LinkedIn, is cluefully participating.