I found an interesting paper on the Measurement and Analysis of Online Social Networks examining  data gathered from four popular online social networks: Flickr, YouTube, LiveJournal, and Orkut.

"…..the indegree of user nodes tends to match the outdegree; that the networks contain a densely connected core of high-degree nodes; and that this core links small groups of strongly clustered, low-degree nodes at the fringes of the network."

One of the reasons to understand the structure of Social Networks is to "…lead to algorithms that can detect trusted or influential users."

One of the findings is for the need of "influentials" at the center of the social network…

"….high-degree nodes in the core are critical for the connectivity and the flow of information in these networks."

Also, Social Networks are very good at helping users (of the Social Network) transverse content - and the case in point is a study of Flickr usage that was done over a year ago in Munich:

"…To investigate the role played by the social network in organizing and locating content, we conducted a simple measurement of how users browse the Flickr system. We analyzed the HTTP requests going to the flickr.com domain from a 55-day HTTP trace taken at the border routers of the Technical University of Munich between August 17th, 2006 and October 11th, 2006. We found 22,215 photo views from at least 1,056 distinct users. For each of these views, we examined the browser’s click stream to determine what action led the user to a given photo.

We found that 17,897 of the views (80.6%) resulted either from following links in the Flickr user graph or were additional views within a visited user’s collection. In other words, in 80.6% of the views, the user network was involved in browsing content. We count these views as being influenced by the social network. Focusing on the remaining  views, 1,418 (6.3%) views were the result of using the Flickr photo search facilities. The remaining 2,900 (13.1%) views were the result of a link from an external source, such as links from an external Web site or links received via email.

Neither of the latter sets of views involved the social network. Our experiment suggests that the social network in Flickr plays an important role in locating content. Over four out of five photos were located by traversing the social network links.

Here's the first gem that I picked out of this paper:

"…It would be useful to have efficient algorithms to infer the actual degree of shared interest between two users, or the reliability of a user (as perceived by other users)."

In other words - the paper has stumbled upon the actual concept of "Friendship" in a Social Network and how it would be measured - the first time I actually came across a workable framework to measure Friendship in a Social Network that might actually be definable by structure of relationships.

Interstingly, such a defination of "friendship" in a Social Network would probably work well for an Online Dating Service - which is selling compatibility of dating partners - but I think the concept can be made to apply to all Social Networks.

Furthermore, the paper outlines that the best way to decimate information in a Social Network is to first give it to the "core influentials" and let is spread out to the rest of the members.

Also "Trust" in a Social Network is defined in a workable way:

"..Our findings have interesting implications for trust inference algorithms. The tight core coupled with link reciprocity implies that users in the core appear on a large number of short paths. Thus, if malicious users are able to penetrate the core, they can skew many trust paths (or appear highly trustworthy to a large fraction of the network). However, these two properties also lead to small path lengths and many disjoint paths, so the trust inference algorithms should be adjusted to account for this observation.  In particular, given our data, an unknown user should be highly trusted only if multiple short disjoint paths to the user can be discovered."

That's a workable thing - one could analyze the structure of the Social Network to come up with a measure of Trust, or real "Trust Rank".

"….The correlation in link degrees implies that users in the fringe will not be highly trusted unless they form direct links to other users. The “social” aspect of these networks is self reinforcing: in order to be trusted, one must make many "2">“friends”, and create many links that will slowly pull the user into the core."