> how are they playing such a significant role on the network?

Well, one thing to note is that, in a global sense, they may not really playing all that significant a role, in the sense that the variance in average path is quite small. I mean, is this Czech fellow's average path length of 2.718 indicative of his actually bringing the overall network closer together that much more than someone with an average path of 2.9? I'm guessing not.

However, that aside, the "best" strategy for decreasing one's own average path will depend greatly on your metric for how "good" a strategy is. For example, Marc's approach of asking other people to connect up might not be a bad way to do it. Certainly trying to just make as many new friends as possible can't hurt. If what you really mean is what would be the most efficient way, from the point of view of greatest decrease in average path with fewest new friends made, then the first obvious thing is to start by befriending the 4-steps-away people... But which ones of the many tens of thousands of people at that distance is the tougher question, I suspect. If one had the whole graph available to play with, I'd venture to guess that a good heuristic might be to start by identifying clusters in the graph, and then befriend a single well-connected member of the largest cluster, then iterate. Or something. (Of course I'm just making this up, haven't really worked any of it out.)

Would you invite me to Orkut, Please ?
None, of my friends are on it.

I was wondering the same thing about "average path length", glad you summarized this. I'll offer my 2 cent shot at gaming it.

The shortest path is between me and one other person, right? So the lower limit on path length should be 1.0. So if an isolated network of four friends all interconnect to each other, the average path of that network should be 1.0. That assumes that orkut isn't doing any black box magic in calculating average path length.

So, to test this, (someone with time can) generate 20 fake accounts and interconnect them (avoiding jail, somehow) isolated from anyone else on the network and take a screenshot before they accounts get zorched.

I really really want to see this put to the test. *eg*

I'm curious what orkut is sorting on when they display community members or people's friends. For some reason, even in large communities, I always show up near the top, but I am not particularly popular or connected. Maybe it goes by newer members, but I think I have been on long enough to be closer to the bottom by now.

Well, guys. The mystics of the average path.

Did you notice the average path is calculated different sometimes ? Because, a week after I first joined, the amount of people I was connected with, dropped 50%. Average path increased about 0.7 points. That was way before there was a stats page.

Then a couple of days ago, average path dropped 0.5, I was suddenly connected to 91% of the people, and that Czech guy (I love the Cezchs! Check with the Czechs!) was the top connector with a below three average.

Hey, I know someone who lost his only friend - so he has zero friends - and his average path is... 1 !

It sure is all about graphs :-) Just read the last paragraph of this: http://www.google.com/codejam/
and you know that they are supposed to calculate the average path :-P

Cheers,
Ace

http://www.orkut.com/Profile.aspx?uid=6185523418686534706

I asked them. Orkut is now sorting friends and community lists by who has logged in most recently. This explains why you generally find yourself near the top of any list.

> What is the algorith to minimize your average path length? Given the data, what strategic connections need to be made for a newcomer?

I could be wrong (again!) but is this not essentially the same problem that Davd Kempe et al. solved a couple of months ago under the title "Maximizing the Spread of Influence through a Social Network"?

Links and my summary at

http://www.cybaea.net/Journal/OptimizeViralMarketing.html

or go straight for the goods at

http://www.cs.cornell.edu/home/kleinber/kdd03-inf.pdf