I just returned from GITEX, the largest IT and consumer electronics trade show in the Middle East, held in Dubai, United Arab Emirates. Perusing Wednesday's Gulf Today, I came across an article regarding Facebook and networks of friendships in the real world. According to Will Reader, an evolutionary psychologist from Great Britain, the number of close friends that one has is essentially invariant, whether one has thousands of Facebook friends or not. Reader indicates that many studies have shown that people have about 150 people in their networks of friends. A small fraction of these are "close" friends, regardless of how big their networks grew.
The reason that this is significant is that it shows several things consonant with my analysis of the statistics of many networks. Specifically, it shows that the connectivity value -- in this case the value of a social connection -- is not distributed equally across all nodes (i.e., friends). This yet again argues against an n squared value for networks, where n is the size of the network, which would require that each connection is of equal value, or at least that the distribution of values has a mean that is a linear function of n, neither of which appears to be the case.
The site now reportedly has over 30 million users, so it also suggests that the number of actual friends and close friends does not change even though the number of potential Facebook friends connections is now substantial.
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