The mathematics of networks
نویسنده
چکیده
In much of economic theory it is assumed that economic agents interact, directly or indirectly, with all others, or at least that they have the opportunity to do so in order to achieve a desired outcome for themselves. In reality, as common sense tells us, things are quite different. Traders in a market have preferred trading partners, perhaps because of an established history of trust, or simply for convenience. Buyers and sellers have preferred suppliers and customers. Consumers have preferred brands and outlets. And most individuals limit their interactions, economic or otherwise, to a select circle of partners or acquaintances. In many cases partners are chosen not on economic grounds but for social reasons: individuals tend overwhelmingly to deal with others who revolve in the same circles as they do, socially, intellectually or culturally. The patterns of connections between agents form a social network (Fig. 1) and it is intuitively clear that the structure of such networks must affect the pattern of economic transactions, not to mention essentially every other type of social interaction amongst human beings. Any theory of interaction that ignores these networks is necessarily incomplete, and may in fact be missing some important and crucial phenomena. In the last few decades, therefore, a researchers have conducted extensive investigations of networks in economics, mathematics, sociology and a number of other fields, in an effort to understand and explain network effects. The study of social (and other) networks has three primary components. First, empirical studies of networks probe network structure using a variety of techniques such as interviews, question-
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