The study of the small world problem by Stanley Milgram provides great incite about the nature of networks and how information travels within these networks. However, the weakness of this study is that it does not take into consideration the density of the networks. The study looks at personal networks, instead of whole networks. Therefore, it is not limited by geographic boundaries but at the same time it can’t provide much information about whether people are using the shortest possible links to reach their target, or whether the incomplete links failed due to errors in choosing the ‘right’ intermediaries vs. the lack of appropriate links between the starting person and the target.
To overcome these problems, the Killsworth study takes the opposite approach and maps out a whole network and looks at relationships within this network through ‘actual’ and ‘conceptual’ paths in order to study the effects of error. This way the problems of the Milgram study are eliminated, yet the issue of boundaries becomes a problem. We still can’t tell if the most efficient chains are formed or not, since people outside this closed network might have been useful in the transfer of information.
Furthermore, this type of analysis is what brings forth the supposed disappearance of communities according to Wellman. As people look at whole networks and realize that they are low-density networks, they assume that communities are disappearing. However, as the Killsworth study itself points out ‘closed systems’ like these cannot be generalized to the global level. So we are still facing a paradox in terms of how to look at networks as we see that both approaches have their strengths and weaknesses.
In scale free networks, majority of the nodes have less-than-average degree and a small fraction of the hubs are many times better connected than others. Lois Weinberg would be one of these hubs, or in other words, a sociometric star. However, it’s not just the degree of links that matters in such a network. The range of those links is also very important. As we see in the Lois Weinberg example, what gives her so much social power is not necessarily the fact that she knows a lot of people but more so that she knows a lot of people who know other people in different networks/subgroups. This also relates to Granovetter’s idea of “strength of weak links.” Instead of maintaining lots of strong ties through “homophily” and “triadic closure” (as outlined in the Watts article) having lots of weak ties allows one to bridge between networks instead of staying within the same network. While the lack of homophily allows a higher range, the lack of triadic closure between links gives extra power to someone like L.W. who can act as a gatekeeper.
Questions:
1) What is the role of in degree and out degree links in regards to the small world problem? Abundance of which type of link would be more advantageous in terms of reaching a target? Is it possible that the discrepancies between in degree and out degree links is what causes chains to break?
2) How would it affect the Korte & Milgram study if they also had ‘negros’ among their starting population, allowing us to compare ‘negro’ -> ‘negro’ and ‘negro’ -> white chains as well?
3) What kind of changes would there be in the Korte & Milgram study concerning racial groups if it was repeated again today? What has changed about our acquaintance networks within the past 35 years in regards to race? class? gender?
4) Is Lois Weinberg more likely to succeed with the Small World assignment on Penn’s campus than someone in our class?