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Review: Identity and Search in Social Networks October 4, 2007

Posted by shahan in online social networks.
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Identity and Search in Social Networks, D. J. Watts, P. S. Dodds, M. E. J. Newman. Science 269(5571), 2002.

The authors have provided a means to predict the length of a message chain when attempting to send a message from a source to a target without having complete topological information, i.e. using only local information. With the intent of being mathematical in nature, they describe how users select their peers based on several independent dimensions, for example, geographical location or profession. The hierarchical structure of group structure is one configuration which can be used to determine relatedness. Peers who are closely related will have a shorter distance based on their lowest common ancestor.

Watts et al. have developed a formula with tuning parameters based on real world experiments dating from Milgram’s experiment that gave rise to the concept of six degrees of separation. They have convinced themselves that because the examined networks have a structure that conforms to a message length amenable to Milgram’s original experiment, then their formula satisfies the required confidence tests. One caveat they raise is that as the number of dimensions increases, the ability to describe the relationships becomes more difficult due to the decrease in correlation between network ties. However; the main benefit of this algorithm is that forwarding a message using an algorithm which brings the message closer to the destination based on a decision of 2 or 3 categories is effective and has been empirically shown.

The algorithm is indicated to be robust for a branching factor between 5 and 10 however I would describe this as being sensitive to the right degree. I would say that robustness has to do with how the algorithm performs in light of failure of part of the network, a case which they have not indicated. Recent experiments from Mislove et al. have shown that removal of the top 10% highly-connected nodes disconnects the graph into millions of small clusters; however, the formula put forth in this paper has an r value, a least probability that a message will reach its target, of 0.05, an arbitrary value which may not apply in today’s networks.

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