http://www.cmu.edu/joss/content/articles/volume2/Bonacich.html

This article was taken from the Journal of Social Structure, an online journal on social structure, and provides an in depth look at almost the exact same information that we have been learning about in class. The purpose of the paper is to do look at the various types of social structures and the way in which they can change over time through the use of computer simulations. It looks analyzes social networks in a manner very similar to the way we have been in class by looking at the gains of each member of the network and finding people who have more power than others (through the use of an exchange game), even coming up with classifications for the position (of power) that a component can have. In fact, some of the structures that the author examines and names are one’s that we have looked at, such as his four-chain and tee networks.

The paper does have points where it differs from what we’ve learned in class, by adding different variants on the way the game is run and the networks are set up. The first thing to notice is that the author does not use nodes and edges to depict the networks, instead using a square grid with each square connecting to a maximum of eight other nodes. Another difference is the way his game is run. The main difference is that his variant allows for the “movement” of the people in the networks - if a person is in a weak position in a structure, it can move away from that structure and possibly form another one with other people. Also, exchanges are made between people only when they get the best offer possible and once they do so, they stop moving. With this game variation and the method in which he uses to depict the networks, he can create computer simulations in which the computer moves nodes and checks for the power of each node according to the rules of the game, depicting the evolution of a the network. A final situation he looks at is the usage of these simulations to model the evolution of bipartite networks, providing a visual depiction of the method of finding market-clearing prices.

The author concludes that the paper doesn’t actually have any analytic results in regards to network evolution and stability. However, the simulations have shown the author several things. First of all, if members in a social network that are not satisfied with their power are allowed to move, most networks will reach a network where the distribution of power is about equal for everyone except for a network in which there are two categories of unequal size(i.e. buyers and sellers). He also found that stability in the pattern of exchanges and profits in networks where there is no movement allowed is present in all networks except those that are what he calls coreless (there is no pairing such that each person is satisfied with his partner). When looking at the stability of the network structure itself, he found that Strong Power networks (networks where there are those who are very powerful at the expense of others) were the only unstable ones. In addition, he found that in non-bipartite networks, those that had an even number of people ended up with indeterminate (network has only slight effect on power - power mainly effected by relations between people) or equal power networks. Those with an odd number ended up with coreless networks. In bipartite graphs, those that have an equal number of people in both categories will end up with indeterminate networks.