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# Social Network Analysis

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Social networks are everywhere. According to Wikipedia, there are over 200 active social networking websites on the Internet, excluding dating sites. As you can see from Figure 11-1, according to Google Trends there has been a steady and constant rise in global interest in “social networks” since 2005. This is perfectly reasonable: the desire for social interaction is a fundamental part of human nature, and it should come as no surprise that this innate social nature would manifest in our technologies. But the mapping and modeling of social networks is by no means news.

In the mathematics community, an example of social network analysis at work is the calculation of a person’s Erdős number, which measures her distance from the prolific mathematician Paul Erdős. Erdős was arguably the most prolific mathematician of the 20th century and published over 1,500 papers during his career. Many of these papers were coauthored, and Erdős numbers measure a mathematician’s distance from the circle of coauthors that Erdős enlisted. If a mathematician coauthored with Erdős on a paper, then she would have an Erdős number of one, i.e., her distance to Erdős in the network of 20th-century mathematics is one. If another author collaborated with one of Erdős’ coauthors but not with Erdős directly, then that author would have an Erdős number of two, and so on. This metric has been used, though rarely seriously, as a crude measure o....