Since I first leaned of the concept of social networks it has fascinated me but I never really studied the topic. It seems to me a huge topic but is not widely studied compared to other areas of mathematics. What better way to study such things as the spread of information, political views, deseases, etc.
In this thread I guess I would like to see a light discussion of a number of ideas within this field and perhaps some suggestion of interesting sources of information.
Looking at the terms defined in wikipedia:
http://en.wikipedia.org/wiki/Social_...twork_analysis
I notice only one measure of distance was measured:
Path Length
The distances between pairs of nodes in the network. Average path-length is the average of these distances between all pairs of nodes.
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Well, this may in some respects be interested given that it is believed that their are only six degrees of separation between most people in the world the number would seem inadequate for modeling the spread of information, disease, ideas, etc. because well, it may only take six steps to connect two people if the path is chosen at random the probability of concecting these two people within six steps could be very small.
6 degrees of separation implies that there are at least (5x10^9)^(1/6)=41 links between each person. Given most people have over 300 friends on there facebook this doesn't sound entirely unreasonable but the number of links between people depends on the type of link. For instance if we were measuring the spread of an std the average number of sexual partners for a man in a lifetime is 7 which is less then 41.
Also my above calculation assumes a very loosely connected network and in this loosely connected network if we take a path of length six there are still (5x10^6)-1 possible other paths that do not connect these two people. Consequently well the shortest path may be close the probability of selecting this path at random is very small.
