Social Network Theory (for March 3)
March 1, 2006
In this week's episode "Protest" (to be shown on this Friday), Charlie examines the relationships among various members of groups organized in California during the '60s and '70s to protest the war in Vietnam. He uses yet another field of data organization made possible by powerful computers: Social Network Theory or SNT
In SNT individuals are represented by "nodes" or dots, and relationships between individuals are represented by lines joining their dots. For example, here is a network of individuals based on whether they communicate with each other by phone or e-mail at least once a week over a period of one year.
This kind of diagram can be automatically constructed by a computer software which is fed perhaps thousands of phone records. The information show by the diagram can be very useful. One of the things we can measure is the degree of a node: how many connections that person has to others. In this example, B, D and E have degree 5, while K has only degree 2.
We also observe that there are two small "cliques": one made up of nodes A though F and the other of nodes F through J. Node F is a natural "connector" of these two cliques, and that individual can serve as as both a liaison or block for communications. Thus, F has a very powerful position in this network.
Suppose this network actually represents a small organization, and the lines represent not just communications but also lines of command, with the individual K being the nominal "director", then we see that K's power is very much dependent on F.
In practice, SNT software can take in vast amounts of data about individuals and various kinds of connections. It then can create all sorts of network diagrams based on weighted combinations of connections. For example: simple communication connectivity may rate a score of 1, while "exchange frequent memos" may rate a 3. Also, there may be lines with arrows, indicating a direction of connection; examples are: "reports to", or "can be fired by." The software can be directed to search for nodes or individuals which have various total scores based on combinations of these connections.
OK, I will stop here: you can make up your own network diagrams that tell interesting stories of communication, isolation, rivalry and power. SNT is yet another example of an application of mathematical reasoning which is not restricted to simply manipulating numbers or geometric relationships. Rather, it is a creative combination of these and other elements to illuminate hidden relationships around us.
For more on SNT, search the web. Here is a good starting site:
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