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Note: I assume that a person is zero degrees of separation from someone they know who knows them, one degree from someone who is in the same state to other people who are zero degrees from him/herself. Surprisingly, I couldn't find a good definition of this by a quick Google search.

Thoughts on : "Ignorance, Knowledge, and Outcomes in a Small World"

the article by Prof. Mark Granovetter, Science Magazine

Volume 301, Number 5634, Issue of 8 Aug 2003, pp. 773-774

http://www.sciencemag.org/cgi/content/summary/301/5634/773#related (requires subscription)

Granovetter's article refers to a previous article in Science about a study of "Small Worlds" (see reference below my text, there is a new experiment underway)

Both articles need to be read before proceeding.

Granovetter's short article is actually a response to an article published earlier written by the academic team that performed the recent "Small World" experiment using email as the contact medium. I participated in the Small World study -- in fact I attempted to reach all of the targets! The first target I was given was one of the study's researchers (although I didn't know that at the time), who is a mathematician. I asked the ONE mathematician I knew, formerly a professor at UC Berkeley, now a professor at CalTech to help me reach the target. And of course, he knew the target. I was thrilled! My first attempt was only one degree away. However, none of the others completed, and not only did they not complete, but almost none of them went past the person I contacted (the initiator of a chain could track the progress).

"This excellent new study raises but cannot resolve the important question of how much people know about their own social networks and why this matters." -- Granovetter

The "why this matters" is key -- for instance, finding out how many people know someone who has a white car who knows someone else who has a white car etc. There's an infinity of information out there and almost none of it is useful or meaningful. Unless you are a hermit, you know people

The issues of node-interest and chain-length made me think of some categories and observations:

There are different kinds of items that pass up and down the chains.

physical items, e.g. viruses, letters (like how people used to give a letter to a person passing thru town and ask him to get it closer to the target) and the modern mail system (including email)
information - e.g. scientists working on a common problem (gene sequencing) and one of them wants to know who has done a particular piece
introductions - e.g. recommendation of a colleague for a job, or introducing two people for a blind date, genealogical searching for distant but living relatives

The node-interest varies widely for these three items, as does the need or lack of need for there to be a feedback loop or a node motivation factor.

For physical items the chain-length is unimportant in the sense that the task can still be done as long as the nodes are properly motivated. Obviously in the case of viruses the nodes are parasites and have their own powerful agenda. There also is no need for a feedback loop for the "task" to be accomplished. For the human nodes, motivation drivers help, in the case of the mail it became a better system to actually pay people to do this work.

For information the feedback loop is very important. The first node is seeking a piece of information and simply having node after node inquire about the data and finally find it does the information seeker no good unless s/he actually gets the data back. In the gene-sequencing chain, all of the scientists have a stake in the outcome so motivating them is easy (unless they are perverse academics who want to claim all of the credit for themselves). Interestingly, I believe the problem Spoke Software is trying to solve is in this category, rather than in the third category of introductions. The sales rep wants a contact name into a company. Unless s/he knows the person who has the contact (or maybe is one degree away) an introduction serves very little purpose as the person doing the introduction cannot vouch for the sales rep. But that node with the contact CAN give the sales rep valuable information like name, phone number, email address etc. Spoke's hiding the nodes is silly, because the path is not important, all that needs to be found is the node with the contact. Having an intro request go thru 5 people means that the motivation drops off dramatically at node 3 and since the target may not want to be found, could even go negative.

Introductions makes sense where the chain-length is short. Ideally 3 with the person in the middle motivated to initiate this activity. In the case of Friendster, the concept doesn't make much sense because the person who performs the activity, the matchmaker, has no motivation to join Friendster although the people seeking a date do. And the current Friendster reputation system, which is simply counts the number of nodes that can be reached by a person, inspires the members to increase their friends with great abandon (like I did) just to appear non-friendless. A better reputation system would measure the number of introductions made, and eliminate the number of reachable nodes as it causes egregious behavior. I also think the genealogical searching for distant living relatives is similar. I have found it very rewarding to connect, and in some cases re-connect, with my second cousins. Our grandparents were siblings and we knew our own grandparents, and in many cases we also knew their siblings. For many of my second cousins we met as children when the grandparents were still alive. So we have a commonality of being at most 2 degrees apart (assuming the grandparents were living when we became old enough to be aware of them). On the Greek side of my family I now know of every second cousin and nearly all of them I have communicated with. This is no mean feat since they live in various countries. As my cousins and I have sorted out who is who, we have also reached back into the parents of our grandparents and found some third cousins. But the interest in contacting these third cousins is very low because they are strangers to us...we really have no common memories. As an extreme example I happened to meet someone who turned out to be "related". How we discovered this was simple -- we happened to meet at a pioneer museum and I casually mentioned that one of my ancestors was the sister of Daniel Boone. The other person said he too was descended from her. And so it was (we checked the genealogy charts that our relatives were working on and they matched up). He and I were sixth cousins! But after that startling revelation --- then what? It didn't make a bit of difference. We might as well have discovered that we both have white cars.

When designing the software for social networking sites it is really important to consider the node-interest (motivation), the chain length, and the need for a feedback loop.